Sometimes the plot demands that you fail. The storyline requires the defeat of the main characters in order to make a point or explain a key event, regardless of whether or not the player would allow their party to fall in battle. There are two ways to accomplish this: One is the Cutscene Boss, where the player has no control over the battle's outcome at all — and the other is the Hopeless Boss Fight.
This is a boss with Nigh Invulnerability, if not sheer invulnerability outright. Odds are good you won't be able to damage or hit him at all — he'll quickly reduce it to Scratch Damage or just ignore it outright as he launches One-Hit Kill (if not Total Party Kill!) attacks on your team, and if you aren't able to run from this battle on turn one, it's Game Over on turn two. Or is it?
These bosses tend to make their appearance near the beginning of the game, before the characters have had a chance to earn Experience Points or Level Up, or otherwise become more powerful than their predefined starting levels — this makes narrative sense as well, because this is when the characters would be least likely to survive an encounter with them anyway. Done well, this defeat will strike fear into the heart of the player, having learned firsthand just how powerful this boss really is; done poorly, it feels like a cheap trick designed to advance the plot, Suspension of Disbelief be damned.
Since games like to pretend to be fair, your opponent in the Hopeless Boss Fight tends to return later in the game for a proper battle. They have the odd tendency to be Climax Bosses: If they were the Big Bad or The Dragon, players will get to fight them after this Final Boss Preview by the end of the game as a straight up Final Boss (or Penultimate Boss).
Ideally, the game should make it somewhat obvious to the casual gamer the fight is probably intended to be hopeless, lest you waste your serious healing items and abilities. This is another reason why these tend to appear at the beginning of the game, as you haven't even acquired any serious healing items or abilities yet.
Often, Genre Savvy players may confuse a hopelessly difficult boss with this and give up fighting on the assumption that the battle is intended to be hopeless ... only to discover it isn't. More fiendishly, some games can silently observe the player's efforts to determine whether they put up a decent struggle before going down, with a genuineGame Over issued if they died too quickly, or make the objective to survive for a fixed amount of time, with any deaths resulting in game over.
Not all Hopeless Boss Fights exist to defeat you at a specific point to advance the plot; there may also be Border Patrol, confronting players who try to go Off the Rails in certain areas with a Hopeless Boss Fight, from which the only option is to Run or Die. If the monster will become defeatable as you gain power, it's a Beef Gate.
Sometimes, the apparently invincible boss can technically be defeated, if you have a precisely tuned tactical setup, access to a Disc One Nuke, the advantage of a New Game Plus or endless hours of Level Grinding behind you. In this special case, defeating the boss may net you a cool reward of Experience Points or rare items.
In any case, since a Hopeless Boss Fight is one the game expects you to lose, the game will react to its defeat in one of several ways:
The Battle Didn't Count, and events unfold exactly the same as if you had lost the battle. Lazy scripting might simply assume that the battle ended with the boss wiping the floor with the party. In extremely rare cases the game may remember this outcome anyway, possibly as a factor for its Best Ending.
You win this fight, but the boss will be back for a rematch and the plot won't advance until you lose to it.
In Castlevania Order Of Ecclesia, at the final battle with Dracula, once you've whittled his HP down to 0, if you're not fast enough to quickly equip the Dominus Union he unleashes an unbeatable move that's supposed to instantly kill you (it does 9946 damage, though if you use the Volaticus Glyph, you can fly in the corner of the screen to dodge it, though the frame of Dracula and the explosion stays unmoving and never ends).
In Castlevania: Lament of Innocence Walter counts until the moment you hit him with Vampire Killer. If you don't and try to hit him with any other whip or attack instead, it'll be to no effect whatsoever. He CAN hit back though so unless you switch to the VK, you'll eventually end up dead.
In Portrait of Ruin, you can't kill the Behemoth during the initial chase, you can only run, even if you are on New Game Plus and could beat the actual boss fight in under half a minute by Dart spam.
Rondo of Blood had the exact same set piece years earlier. The Behemoth in Rondo could be defeated, though.
In American McGee's Alice, Alice cannot defeat the Jabberwock the first time she fights him. The objective of the battle is survive and stall until the Gryphon can arrive to chase him away. (Succeed, and you get the final component of the Jabberwock Eye Staff, a powerful weapon.)
Shadow of the Colossus has an unusual take on this: At the end of the game you turn into the final boss, you're effectively invincible and can attack the armed group that just tried to kill you. This is hopeless, though. They'll seal you away no matter what you do.
killer7 brings two semi-examples to the table, the first being the fight with against the Handsome Men (essentially a series of duels, some of which are impossible to win, and in the long run you only win thanks to one character's Eleventh Hour Superpower) and the other being the fight with Greg Nightmare (who sends a group of near-invincible Heaven Smiles at you, who systematically take down six of your personas, leaving Garcian to pick up the Golden Gun and finish Greg off).
Oddjob from James Bond 007 for the Gameboy could not be beat without a special item, ensuring Bond gets dumped in the desert where he can't possibly survive.
Brave Fencer Musashi has the fight with the super-vambees in the church. They can't be killed by damage, and if they grab you it's instant death. Fortunately, if you hold out long enough, the sunlight kills them. There's also a few instances where there's some invincible thing chasing you and all you can do is run - the stone head in the prologue chapter comes to mind, as does one of the forms of the Final Boss.
In Ys Seven, there's the first fight with Scias in Altago Palace where you MUST lose after his HP is at half, since ALL attacks are BLOCKED (0 Damage) from then on ALONG WITH an attack that does 2k+ damage to you.
In Ys Origin, when played as Yunica, the first fight with Kishgal definitely counts.
In Pokemon Rumble Blast, at the end of World 2, you get a Team Battle with one of these. Lampshaded with a Help Sign stating that "things might not always go your way, but sometimes is a good thing." Hurts your pride if you don't read the sign, but is considered a Critical Hit after winning the Charge Battle to reach this zone.
At the beginning of the game, the boss fight is against Zekrom, the Penultimate Boss fought right before Dark Rust. Because of the nature of the game, it would be possible to defeat it - except it destroys the floor of the arena and flies away after either you or it take a set amount of damage.
In Pokemon Rumble, at the beginning, Rattata notices that the boss door is open and sneaks in. Of course, you can't win with level 28 against 100.
Kratos's first encounter with Zeus in God Of War II, where Kratos is tricked into draining his godly power into the Blade of Olympus, rendering him mortal. After the battle with the Colossus, Kratos is heavily weakened, barely able to swing his blades. At this point Zeus comes along and defeats Kratos.
Similarly, in Chains Of Olympus your first battle against Charon is hopeless, since you don't have the right weapon to fend off one of his attacks. You must cross all Tartarus to find it and get back to fight the boss.
Blood Omen: Legacy of Kain includes an early battle with Malek. He cannot be killed, forcing Kain to leave and seek help, first from the oracle (Moebius) and then Vorador, who defeats Malek himself.
In fact, the very first battle is against respawning bandits. If you kill them all, more will come along, and eventually kill you in order to progress the story.
In Dantes Inferno, you may perceive the first level's boss, Death, to be a hopeless fight (understandably so, seeing as he's Death), if you don't realize that his life bar decreases from right to left, rather than the standard left to right. In reality, he is a Wake Up Call Boss, teaching you the importance of blocking.
This happens twice in Breakdown, both with The Dragon, Solus. The first time isn't much of a fight, since he slams you against a wall before you can really do much. The second time is more of a fight, but the second he gets more strength, the fight's basically over. However, you get to fight him again after some Time Travel, and after he remarks that you were supposed to die quick, you beat him because you're now as powerful as he is.
If you play the Zeon campaign in Mobile Suit Gundam: Federation vs. Zeon, nearly every encounter with Amuro and his Gundam is this. You're not even able to consistently damage him until the final mission, where you drop into his own final battle with Char.
Same with Char when playing the Federation side. Note that is is actually possible beat both of them during these Hopeless boss fights, it's just very difficult and doesn't change anything.
Eureka Seven has two videogames, the first of which has you get pit against a high level pilot before the tutorial runs. You are able to beat her with the correct amount of effort, but your first time playing you will be severely unprepared. If you do win, it doesn't matter anyways, it only changes the following cutscene a little and everyone still treats you like the newbie afterwards while Ruri is still hailed as the best.
Fullmetal Alchemist: Curse of the Crimson Elixir has the boss fight with Scar. Win or lose, the same exact cutscene happens where Ed and Al are defeated. If you win, you do get an item at least, but it doesn't change the story progression. Neither does the following battle with Armstrong, but that doesn't affect anything but the direct moment anyways.
The very end of the game, after you've beaten the final boss, pits you in a hopeless boss fight against both Mustang and Armstrong at the same time. You can attack and dodge them all you want, but they can't be defeated. You can knock them out, but they'll just get back up again a few moments later. You're intentionally suppose to lose.
Custom RoboArena: The second time you fight Hadron, he is totally invincible, as he has completely absorbed Scythe's energy. You have to lose to trigger the next scene. Also, in a dream sequence at the very start of the game, you fight Jameson of all Robos. Technically, it's possible to win, but the dream ends a short while after the battle starts anyway.
The first boss battle of Metal Gear Rising Revengeance has Raiden facing off against "Jetstream" Sam. Sam does fairly devastating damage, even when the player blocks his attack and can also Flash Step away. Also, in the first and second phase of the final battle Raiden can only do Scratch Damage to Armstrong at the best.
Escape from Monkey Island ends with a Boss Battle that could go on indefinitely, as the players regenerate their hitpoints faster than the other can take them away. Naturally, there's a trick to winning this one.
In chapter 2 of Imprisoned, you have to kill two guards in a row, and then the third fight is against a machine, which you can't damage. Later on, with a special ring (and/or a whole lot of Level Grinding), you can beat them. The fight with Jade is similar in that you can't damage him because he needs to beat you for the game to continue.
The flash game Armed With Wings 3 has a battle with the evil king Vandeer Lorde as the third boss, which you're plotwise not powerful enough to kill by then. He gives you 30 seconds to live, so the boss battle ends after those 30 seconds with a cutscene, and the goal is to survive. A little annoying since he's not all THAT tough, and it would be possible to actually kill him, especially if you use a New Game Plus. Makes it all the more satisfying to kick his ass when he returns as the final boss, in pretty much the same state.
At one point in Cosmic Spacehead you find yourself in an asteroid field and are told to keep dodging the incoming rocks. The action sequence continues until you take too much damage, at which point you are forced to take a scripted stop at a space station. Unfortunately it's quite easy to dodge every asteroid that comes your way, which means that a good player may end up continuing the sequence indefinitely, or at least until they get bored and decide to throw themselves into a rock on purpose.
Card Battle Game
In the DS Dinosaur King game, one of these is fought against Seth-he counters every move you can make regardless of what you do. A variation occurs in that it occurs after a normal boss fight with him.
Somewhat unusually for a Yu-Gi-Oh! game, Yu Gi Oh Forbidden Memories has one of these, the first time you encounter Heishin. If you do manage to beat him, he simply challenges you again. (And again, and again, and again, if need be...)
In Monster Racers, you face off against world champion Reinhart in Ayers Rock shortly after winning the Star Cup. He has a level 35 Furion, whose stats are far and away higher than any of your monsters at this point, and it will outrun you effortlessly. You won't lose any Will for losing the race, and Reinhart will praise your effort in spite of your loss.
In one case for Need For Speed: Carbon, you can't ever get away from your pursuer in the very first race.
A very bizarre example exists in the Megadrive/Genesis port of arcade game Super Monaco GP. G. Ceara, who is in no waysupposed to belate F1 legend Ayrton Senna is supposed to be set up this way. He appears during your second racing season and is supposed to defeat you in the first few races no matter how fast you drive until you lose your contract to drive the best car in the game. Upon doing that, he will then become beatable normally for you to earn back your position with the top team. However, the way he's coded, if you can drive a string of perfect races early on, you can defeat him and bypass this entire scenario. Nothing changes except that you don't change teams.
Racing Lagoon, a battle against Kyoji Nanba's monster RX-7 is likely to be unbeatble. It's possible to win with a lot of turbos, but the result's not different.
Forza Horizon starts with you racing festival champ Darius; it's also the tutorial, so the best you can really do is stay on his tail.
In the arcade version of the Fighting GameRival Schools, you start off fighting students from other schools, attempting to uncover the mystery behind a rash of student disappearances. But in the third round, Raizo, the principal of Justice High School, shows up with a brainwashed person (his partner for the 2-man special attacks) to fight you. True to the trope, Raizo is very powerful and extremely resistant to damage at this point, but with enough skill, you can manage to chip off enough damage from him and fend him off until time runs out. If you lose as the plot demands, you continue to fight other students and unravel more of the story. If you are playing as the two Justice High teachers and lose, you still continue to fight students... as a brainwashed agent for Raizo, complete with color-changed outfits, until the plot has your adversaries fight you to snap you out of it. On the other hand, if you do beat Raizo here, you skip directly to the end of the game, with another fight against him (depowered to beatable levels, of course). Either way, once you defeat him you then fight The Man Behind the Man, an Ax Crazy, sword-wielding Justice High student named Hyo.
Slightly different with the Gedo High in which Akira fights with her teammates instead (probably vice versa if the player is controlling Edge or Gan...I don't remember). However, the said opposing teammates still take less damage than usual. They are quite beatable though if you actually take the time and are careful enough not to get hit too much.
In several wrestling based games, there are matches where, even though they are hard, you can easily win. However, due to the storyline calling you to not have "come out on top" or not possess a certain title, a cutscene will play that takes the title/glory away from you. Several examples in Smackdown vs Raw 06 include: HHH losing in a steel cage, but Eric Bischoff taking away your title, defeating Eddie Guerro but the Undertaker interrupting the match, winning the tag team title, but having to give it to the injured wrestler you previously replaced.
The original SmackDown vs. Raw has a big example itself. At one point, you are given the option to join Vince McMahon, who will referee a WWE Championship match you're in. If you take his offer, it is impossible to lose as he will not recognize submissions or count past two when you're pinned. The inverse, however, is that if you turn him down the same goes for your opponent, meaning it's only a matter of when you lose.
You CAN win the fights, if you're extremely good at dodging, and very patient. But the cut scenes take place like it never happened, since the cut scenes are right out of the anime.
Dragon Ball Z Budokai Tenkaichi 2 plays with this. Certain fights are normally impossible to win, and losing them advances the plot. However, level up your characters enough and you'll be able to alter the story's progression by winning. This opens up alternate story paths that shift around events and characters, the results of which are often hilarious.
Dragon Ball Z Hyperdimension for the SNES has fights in the story mode which you are intended to lose but with enough skill you can win these fights, however winning these fights has no effect on the story and the characters act as if you lost regardless.
Magical Girl Lyrical Nanoha As Portable: The Gears of Destiny: The earlier battles against System U-D are like this, though they're beatable with enough skill. If you do manage to win, it will be revealed that the now exhausted character did little to no damage to System U-D, with the story continuing as normal after U-D retaliates. Having said that, beating her during these Hopeless Boss Fights is one of the prerequisites for accessing the Playable Epilogue and unlocking System U-D as a playable character.
In Duel Savior Destiny these get pulled on you more frequently as you get into the later story routes. For example, having to go up against four boss units at once all by yourself. During the last route, the game even dumps characters you've never had a chance to use or even have as your ally before, apparently expecting you to lose. If you don't, the game just undoes your victory anyway so you can win the way it wants you to.
First Person Shooter
Deus Ex has a well-executed instance of this, where you are confronted by a small army who demand your surrender, led by Gunther Hermann (a main character). You have the option of resisting (even if this is obviously foolish), but Gunther is invincible in this fight, so there's no way to avoid getting captured even if you manage to outfight everyone else (which is pretty hard to do, so you will likely not even notice Gunther's invincibility). You get to fight Gunther later, when he's quite mortal.
It is quite possible to be starkly confronted with Gunther's invincible nature by taking advantage of his ridiculously stupid AI; lure Gunther into the train station and make an escape through the tunnels. Destroy the small army of UNATCO troops and bots awaiting you, and then find out (to many tropers' eternal frustration) that even though you can hear the evac chopper waiting for you, you can't get to it; you're forced to battle Hermann.
It is actually possible to get to da choppa by putting LAMs or gas grenades on one of the shack walls, and then climbing them. If done properly, this will get you past the invisible walls and invisible ceiling and you can get to Jock's copter. Even if you do this, he will still completely ignore you, forcing you to either kill yourself to continue or load from an earlier point.
If you trap Gunther in the train station as mentioned above, and manage to survive the other troops and bots outside for an extended amount of time, the game will move to the next plot point anyways just as if you had surrendered or been knocked out.
The climactic battle in the sequel to Star Wars: Dark Forces II: Jedi Knight, Mysteries of the Sith, presents a unique Hopeless Boss Fight when Mara Jade fights Kyle Katarn (now seduced by The Dark Side). Kyle's attacks are normal, but he is entirely invulnerable and hence impossible to defeat. This situation almost counts as a Puzzle Boss, except that the solution is not a test of wit.
Jedi Knight II: Jedi Outcast gives another example. Justified in that, alas, he has Force powers and you do not.
The justification is even better than it sounds, because theoretically he has an unbeatable counter to any kind of attack you use. Blasters and energy weapons? Deflected by lightsaber. Thrown explosives? Force Pushed back. So it's not likely the player will even get the chance to verify he's invulnerable as well.
Of course, if you happened to be less than skilled and used a cheat code to make yourself invincible, the game becomes unwinnable, since neither side can die.
In the last fight in this game you can reverse this trope on Desann (though it is hard). This is possible by trapping his lightsaber under the weak pillar in the room by making it fall on top of it when Desann uses a saber throw. He will then be unable to defend, and only use his force powers to force pull his saber, which is stuck.
Kinda like this in Jedi Knight III: Jedi Academy. You have to defeat a mutated rancor. And when you do, the game respawns it immediately. If you do follow the (not so) logical level layout, you can get to the scripted ending where it dies for real.
The same goes for the level where you have to distract a rancor so the prisoners can escape, and you escape as well in the end. You can actually kill the rancor, but the game respawns it immediately.
When you first encounter the Makron in Quake IV, you can't beat it. You can die trying, however; unless you let the Makron catch you with its gravity beam, and thus capture you alive.
Sometimes the gravity beam glitches and kills you anyway (perhaps by wanting to drag you through scenery):
Notable counter-example: in the original Halo, there is a scene where several waves of enemies (but no boss enemy) are used to herd the character through a scripted scene. Perplexingly, however, the enemies aren't unlimited, and it is possible on the lower difficulty levels to beat them all, while Cortana keeps telling you that the only safe way out is to jump...
Played straight with the post-credits Last Stand mission in Halo: Reach, where you fight increasingly tough waves of enemies until Six is killed.
In Half-Life if you refuse the G-Man's offer at the end of the game, you materialize in the middle of a Vortigaunt building with an endless number of enemies...and no weapons. Additionally, both of the first two gargantuas encountered were apparently intended to only be beaten by luring them into a power reactor and an airstrike respectively, but through an oversight (likely to make it vulnerable to the airstrike), if you hit it with enough ordinary explosives you can kill one early.
While not technically a boss fight, a scripted event early in Half-Life 2 forces you to be overwhelmed by Combine forces before Alyx saves your sorry hide. It's impossible to skip this or defeat the Combine soldiers because you don't have access to weapons that early in the game. If you use a cheat to give yourself weapons early and kill the soldiers before they wail on you, the event doesn't trigger and you're stuck in a small corridor with nothing to do.
Midway through Half-Life 2: Episode 2, you encounter the acidic antlion queen in the antlion lair, who cannot be hurt until you're back outside later in the game.
According to the commentary, not only were you not supposed to fight the Guardian in this section, as a general rule you didn't have enough ammo to actually kill it. That didn't stop playtesters from trying, though, so they had to add a line from the Vortigaunt expressly forbidding you to kill it so that you wouldn't try.
In Call of Duty 4, during the end mission, You are told to shoot down a pursuing helicopter. Naturally, you can't.
In Rise of the Triad, your first fight with El Oscuro cannot be won by simply shooting at him until he falls down. Firing at him will cause him to mirror your attack with a magical variant of his own. Just wait it out, avoid his attacks, and eventually he'll run away and trigger the next level.
The first level of the time-traveling FPS Darkest Of Days has you as a member of General Custer's cavalry during the Battle of Little Bighorn. That goes about as well as you would expect.
Episode 1 of Doom ends this way (as does one level of The Plutonia Experiment if you choose the wrong one of its two exits); you get teleported to a dark room full of monsters, with a floor that not only drains your health but also turns off the god-mode cheat if in use, and you can't move; apart from shooting the monsters, all you can do is wait for your health to drop to below 11%, which ends the game.
The beginning of the ruined zoo in Super Smash Brothers Brawl has the Porky Statue from Mother 3, which cannot be defeated... well technically not. Without cheating, using Smash hacks, or somehow changing his absurdly massive HP, you can and will never manage to deal nearly enough damage to it to break it.
In Battlefield 3, during the second and final mission as Miller, you have to hold out for an evac helicopter to come save you and comrades from your disabled tank with its .50 cal machine gun for 15 minutes. It's impossible.
In Far Cry 2, you start the game trying to flee a town while a civil war is going on all around you. You can't successfully escape the town, because even if you avoid getting killed by gunfire, you collapse from malaria before you can get far. Once you're out of commission, one of the factions picks up your semi-conscious body and drags you to safety to get you to work for them. Which makes very little sense, considering that you may have just shot a lot of them... and then either lost, or collapsed from your terminally serious case of malaria.
Anubis from Zone Of The Enders is unbeatable, and that's it. A rare example of the final boss being such. While you can just wait for the end of the game to happen, if you are fast with the controls you can avoid any damage from him whatsoever, at least on easy. The only damage taken is that in a cutscene about halfway through the battle. What makes the battle that much more frustrating is that you spend the entire game (which isn't very long, mind you) fighting bosses that condescend and belittle you for being a kid, despite wiping the floor with them time and again. What do you learn when you reach Anubis? They were right. It is literally impossible to land a hit on the thing because it teleports from place to place constantly, away from you and dangerously close; but, to make matters worse, it can kill you if you're foolhardy enough to try to take it on (or are playing on the higher difficulty levels). The only option is to wait for the Atlantis to save you and run away.
Then he returns in the sequel and is unbeatable again the first time you fight him. The difference here being that it is actually possible to inflict some damage to him during the battle. Unfortunately, you're still too weak to take him on fully. It isn't until the very end of the game, after getting the same teleportation ability that it has, that you actually can win, and it is Satisfying .
In EverQuest Kerafyrm the Sleeper in the Scars of Velious expansion. He had insane HP and attack power for the time on top of the death touch ability. He was not intended to be defeated, instead utterly destroying your raid party and the inhabitants of Skyshrine, then disappearing from the game until he resurfaced as the killable Big Bad in Secrets of Faydwer.
That didn't stop the top three most powerful guilds on the Rallos Zek server from uniting together in 2003 and proving to the entire world that he was technically killable. Zerg Rush tactics worked out quite nicely. His corpse had no loot.
Final Fantasy XI has Absolute Virtue. When it was first released, it was supposedly killable ("the Development Team killed it with 18 people"), but anytime players have managed to kill it Square has nerfed the method that they used within weeks. Worse yet, their released information on how they killed it required violating their own TOS. For a long time, it remained this; however, Absolute Virtue is now defeated on a regular basis by many linkshells.
Another megaboss, Pandemonium Warden, also fit this category; in fact a story of a linkshell fighting it for several hours and finally submitting to fatigue and other personal needs became newsworthy when the boss was first unleashed.
The final mission of the Statesman's Task Force in City of Heroes features Lord Recluse, who's sucking the power from every hero in Paragon City, except you and your team, via four collection towers. He is completely impossible to defeat while the four towers remain standing. He can barely be hit, and if he is hit, he takes little damage, and he regenerates more health in one second than it would take a team of 8 damage dealers to do in a minute. And he can one-shot most tanker-type characters.
Also: (ISSUE 15 SPOILERS) In the new set of Task Forces, the Arch-Villain Riechsman takes no damage the first time you see him. You spend the next few missions devising a way to damage him, then put your plan into effect in the last mission. Even then, he's no push-over.
Mabinogi Fantasy Life: In G13 (Hamlet), you are instructed to fight the Grim Reaper, who is trying to kill Shakespeare. However, this is impossible due to the Grim Reaper's high immunity.
World of Warcraft has a variant in this in the Halls of Reflection. The boss is impossible to kill but the encounter is more about running away from him and killing waves of his minions fast enough before he catches up to you and kills everything in one hit.
Sort of repeated with Arthas in Icecrown Citadel. He instantly kills everyone when his health reaches a certain mark, but it's not over yet... King Terenas' spirit breaks free from Frostmourne and brings everyone back to life, while also weakening Arthas to the point of being a free kill.
The Vizunah Square mission in Guild Wars: Factions ends with Shiro Tagachi showing up and killing the entire party. It's not over yet, though, as the Envoys appear to resurrect you and explain the situation. This can be a problem, however, as the any necromancer minions (which generally prove very useful in the rest of the mission) have become unbound when the necromancer died and are now wailing away on the resurrected party while the leader chats with the envoys. Parties have been known to wipe this way.
Phantasy Star Universe has one of these in the first chapter of episode 2. The battle against Ethan and Liina is impossible as you cannot deal any damage at all. All you can do is endure long enough for a cutscene to take over.
Similar to World of Warcraft, the "Whisperdoom's Spawn" adventure in Dungeons & Dragons Online includes a section where you have to destroy the giant spider Whisperdoom's eggs while avoiding the spider herself. On normal difficulty, she's level 11 (the quest is level 6) and has massive damage reduction and a Healing Factor. It's best not to attack her directly and just smash the eggs.
Fisher-Diver has Captain Connel who cannot be damaged. He eventually kills the player. You cannot escape him either as the oxygen supplies stop working when trying to return to surface.
Dangan Ronpa technically has "culprits", not "bosses", but the trope plays out the same way in chapter 5. You cannot solve chapter 5's murder, at least not in chapter 5 itself. This is because only the player character, Makoto Naegi, and Kyouko Kirigiri are the suspects in that case. At one point Kirigiri tells a lie in court, but if you reveal it Kirigiri is executed and you get a bad ending. But not revealing the lie causes you to get executed...only to be saved at the very last second by an outside source. So chapter 5's "boss fight" is hopeless because you cannot win. You can only progress to chapter 6 if you lose in the correct manner.
Vile, the first boss of Mega Man X, is unbeatable, and in order to advance in the game, you have to let him beat the crap out of you. A similar situation happens later on in the 1st section of the final level, but Zero sacrifices himself so that you can fight Vile without having to deal with his indestructible giant mech.
With patience it is possible to survive the fight with Vile, but he still doesn't see you as a real threat and only leaves when Zero shows up.
When you are down to low amounts of health, Vile will try to jump away and shoot a paralyzer beam. If you're skilled enough, you can dodge the beam, run into Vile, and take enough damage to die. Take That Capcom!
In the remake of this game, Maverick Hunter X, you can beat Vile very easily, and you are in fact required to do so (he'll kill you easily, no paralyzer beam this time), but he uses what basically amounts to a sucker punch to achieve the same situation in the original game. In the rematch, the Hopeless Boss Fight is skipped entirely and goes straight to the Heroic Sacrifice, which then leads to the mano-a-mano.
Similarly, in Mega Man and Bass, the first real fight with King is unwinnable, requiring Protoman to perform a Heroic Sacrifice, enabling you to actually hurt King. Like Zero, Protoman doesn't die for real. Even though he was cut in half in the opening minutes. Yeah. An axe, in a game full of shooting things. Incredible, isn't it?
Your first fight with High Max in X6 is unbeatable; you just have to wait out his attacks until a cut scene triggers.
Given how the game was designed, any of the times you fight him with X after the first time can be unwinnable because it's possible to fight him before getting a way to damage him. Except the fight never ends after the first time and you die if you lose.
In Super Metroid, the Mother Brain begins as a hopeless boss fight, indestructible and using a wicked beam that pins Samus against the wall. After reducing her to 1HP and preparing to fire again, Samus' baby metroid from Metroid II attacks it, draining it into helplessness, then feeds that power into Samus to restore her. The Mother Brain awakens and kills the metroid. An angry Samus (and likely an angry player) then opens the proverbial can with a new blaster weapon - the Mother Brain's super-beam, which smacks it around like a tetherball.
You still have to fight well enough to survive her uber-attack at least once, and you have to do enough damage to trigger the uber-attack (Mother Brain will not use it until she's taken a lot of damage). If you don't survive the first one, the cutscene will not happen and you just get a standard Game Over. If you do really well, you can survive this attack multiple times, but the battle remains hopeless until your energy has brought down low enough for the cutscene to take place.
Ridley at the beginning of Super Metroid is also nearly impossible to beat: You can take enough damage (until you are below 30 Energy, more specifically) or hit him 100 times, whichever comes first, since both events cause him to fly away. There's an amusing little twist on this one: if you do manage to hit him enough times, he will drop the Metroid briefly before picking it up, suggesting you at least hurt him.
Likewise, at the end of Metroid Fusion, you face the Omega Metroid, and must let it claw you down to 1 HP, at which point the erstwhile Big Bad, SA-X, attempts to kill the Omega Metroid and is struck down with one blow, giving Samus the chance to absorb it and regain the Ice Beam.
A really strange version occurs in Revenge of Meta Knight, one of the games in Kirby Super Star. The first time you face down Heavy Mole Lobster on the ship, he actually isn't invincible to your attacks or strong enough to KO you with one hit. Your attacks are effective as normal. However, while you're fighting, Meta Knight is having a dialogue with his crew on the bottom of the screen. The dialogue doesn't last very long, and the second it ends, Kirby gets blown off the ship. So the player hypothetically could defeat the boss, but there isn't nearly enough time.
If you are really fast, skilled, dodge every attack without taking damage, never cease damaging Heavy Lobster, and have an appropriate weapon, it is just barely possible to kill it before you're blown away. Of course, because Heavy Lobster is only really meant to distract you at this point long enough for said blowing, it changes nothing.
In the Meta Knightmare Ultra mode of the remake, Kirby Super Star Ultra for the DS, you actually do have to beat the boss, both here and at the later point in the game where you'd face him for real as Kirby.
Drawn To Life: The Next Chapter's final battle with Wilfre must be initially lost to continue.
You Have To Burn The Rope subverts this trope. Your normal attacks can't harm the Grinning Colossus enough to even remotely get his healthbar down, but on the other hand once you burn the rope, you give that Colossus a one-hit kill.
The Legendary Starfy has one in the final world before you defeat Mashtooth for the first time. Starfy's Dragon form is useless against Mashtooth, becuase Mashtooth has a flippin' sheild! So the battle must be lost in order to continue, where you battle Mashtoth for real as normal Starfy. This does not happen after defeating Mashtooth for the first time, not even in the boss rush, for it skips to Normal-Starfy-Versus-Mashtooth fight.
The fist fight with the Great Devil in Adventures of Lolo 3, 3/4 of the way through the game, is unwinnable. There's nothing really to indicate that you can't beat him, the only hint being that the manual says there are 3 sections of the game, while this fight takes place in the 2nd section. Not so bad, since there are no items for you to waste, but has the potential to be a nasty surprise if you thought it was the final boss, only to discover that there are still 25 more levels before that. Not to mention that his only attack is firing very easy-to-dodge projectiles, which means you could keep up the fight a long time without realizing it was useless.
Real Time Strategy
The second Bavakh Brother in Immortal Defense, who ends up destroying all life on your homeworld. It turns out it is possible to beat him, if you're crazy good and crazy lucky, but even if you do the game continues as though you hadn't.
Warcraft III involves enemy heroes with Divine armor, which can only be destroyed by units with Chaos damage. Because no ordinary units in those scenarios have Chaos damage, the bosses are invincible. Examples include Mal'Ganis, Cenarius and Tichondrius. The player must seek a power-up to gain the Chaos damage required to kill the boss and win the scenario.
Mal'ganis is not an example, as he does NOT actually have Divine armor. He is basically a normal Dreadlord hero, he will attack your base as such, get killed as such, and resurrected upon the Altar as such. Frostmourne may give Arthas Chaos damage, but he is really not necessary to beat the mission - the point is to destroy Mal'ganis' base rather than killing him. Cenarius and Tichondrius are straight up invincible, and can be killed only by the Orc army after it drinks the blood of Mannoroth and Illidan when he uses the Skull of Gul'dan, respectively.
Then played dead straight in final mission of the original, which is basically a Hold the Line mission. You cannot hurt Archimonde (at least without using cheat) as you are only supposed to keep his army from reaching Nordrassil gate until the time runs out.
Incidentally he's easily killable with the godmode cheat built into the game engine itself. However, even after the destruction of Archimonde and all of his forces, the scenario still proceeds as normal (so if one of your ally bases gets destroyed, you will see the pre-programed cutscene of him gloating about it). However, all cutscenes will not have him anymore, as it utilizes his in-game model to do so. This ends up hilariously having a glowing circle on the ground gloating at you and causing all the destruction in the ending. The absolute final cutscene, however, is a pre-rendered CGI video, so Archimonde will appear as normal.
Similarly, one of the early missions in the Human campaign has you having to defend a small town against endless waves of undead. Given the small amount of resources, upgrades and units that you can use to set up a decent defense, you can never actually destroy the two undead bases that keep sending their spawns at you. By the end of the mission, not even a perfectly positioned series of towers and soldiers can stop the undead from overwhelming you. To make matters worse, there's a side-quest in which you have to prevent a THIRD undead army from being spawned.
In Pikmin 2, the Water Wraith. The game's Ninja Butterfly even tells you "Run Away! Run Away very Fast!" Any attacks against it result on the Pikmin being killed until the last sublevel of the dungeon when you recruit the purple Pikmin and can make him tangible.
In Kingdom Under Fire: Crusades, during Gerald's campaign, you supposedly get one of these against Regnier. Your commanding officer tells you to flee the fight and protect the king. Its only supposedly hopeless because you can actually beat Regnier's unit by having your archers heal you and fire into the melee, while your infantry charge in, steal a few technique points (enough to heal) and then high-tail it back out. This allows a level 7 Gerald and level 9 Hugh to defeat a level 50 Regnier. You still have to leave the battle though, and it doesn't alter anything. (Though you do get a ton of experience.)
Happens later on while trying to sneak past a massive army of level 50-100 orc units. You're supposed to go around them. Sneaky players can lure them off one at a time and defeat them using the paladins you have with you to heal. The dark elves which try to nuke you with meteor spells are, however, invulnerable, and your only recourse is to dash past them. This leads to the incredibly frustrating situation where you've beaten around five units of ridiculously high level orcs and swarms upon swarms of weaker enemies if you went to wipe out every last enemy on the map, only to get blown into oblivion by some stripperiffic"vellie" mages. Gosh Dang It to Heck!! Again, you get gamebreaking amounts of experience and gold for this. Just as well, as the hardest battle in the game is just around the corner.
Similarly, in Ellen's campaign there's a mission in which you're supposed to just run past several armies of ecclesian knights and paladins. While you can attempt to take them on one by one, you're constantly being chased and spammed by the spells of the paladins, so fighting is not quite a viable option.
Starcraft: Terran Mission 3 is supposed to be a hopeless fight, with your goal being to survive half an hour. Unfortunately, the Zerg bases were somewhat less robust than that would suggest. Terran 9, on the other hand, features a genuinely indestructible Zerg base, because destroying any of the buildings ends the mission (It Makes Sense in Context).
That is still a victory, because survival is the objective. In the Starcraft II: Wings of Liberty mission "In Utter Darkness" the ultimate fate of the Protoss (and Zerg) is to be annihilated. Your mission objective is to hold out as long as you can until the inevitable end, where you must be wiped out in order to 'complete' the mission.
Two levels in Homeworld 2 have you facing off against Progenitor Keepers, incredibly advanced drone warships left behind by a Precursor race millions of years ago and who've taken a disliking towards you for having stolen one of their ancient artifacts. The player's most powerful weapons will barely dent a Keeper, and once worn down by attrition they simply hyperspace out and reappear again with full health. It is then up to the player to stay alive against this onslaught until the game script eventually bails him out of the situation.
The First time you fight Purge the Great in Space Channel 5 Part 2, Ulala is only able to dodge deadly lightning attacks. After giving you some truly Nintendo Hard commands, Purge goes and kills Ulala.
Gitaroo Man contains two examples. On the way to Planet Gitaroo, your ship is ambushed by a giant robot shark, and all you can do is dodge until you unlock a Humongous Mecha to fight back with. Then, the Big Bad kidnaps your dog (who helps you transform) and the player has to dodge attacks from the Sanbone Trio until they accidentally free him for you.
Pokemon Mystery Dungeon: Gates to Infinity has this at the final boss. When you fight Bittercold alone with no partner to help you, you can't do any damage to Bittercold, until you are aided by The Power of Friendship and eventually you literally Use Your Head to reveal the core, and then you fight Bittercold for real.
Early on Disc 2, you may choose to grab the Key from Valna and Vigna (the two little girl mummies) without having their dolls (accessible later in the game). None of your attacks will have any effect and you'll be forced to escape unless you want to die.
At the very end of Disc 2, while you're in the Church Nave area, a Gargoyle appears and manages to separate Koudelka from Edward and James. A fight begins, but none of Koudelka's attacks reach the target. The only way is to escape and, optionally, take it on later when reunited with your friends.
In Chapter 3 of the second game, you can't beat the Iron Clefts the first time you fight them. After they beat you, you get a new party member, a Yoshi, who comes with an ability that can damage them — at least, when the game's working properly.
Finally, in Chapter 4 of the second game, you have multiple encounters with a ghost who has stolen your identity (don't ask). Until you discover his name, he can't hurt you and you can't hurt him.
His name is the same every time, but interestingly enough the same place you find his name is the same place you find the missing letter in the name-entering screen.
This is done on purpose, because he asks you to guess his name earlier in the game, but people who have already played (or read a guide) know his name when Mario shouldn't. So they removed a letter from the name-entering screen so whether you know his name or not, you can't enter it until you find out his name in-game.
Don't forget about the Shadow Queen, who until Peach intervenes, is basically invincible.
In Mario & Luigi: Partners in Time, Mario and Luigi must fight three Shroobs near the beginning. However, the Shroobs are aided by a giant bomb-carrying UFO that destroys the brothers after three turns, making the fight impossible to win. The intention is for Baby Mario and Baby Luigi to then come to the rescue of their adult counterparts, the UFO being removed in the second fight. If you are to use an Action Replay, the game will act as if you lost.
In Mario & Luigi: Bowser's Inside Story Bowser's first fight is with Midbus in which you learn how to fight. Then Bowser starts feeling weak because of the Vacuum Mushroom and loses. However, if you beat Midbus with an Action Replay, you get no experience or coins, and the following cutscene just acts like he defeated you. In that case, it makes the bossfight a Heads I Win, Tails You Lose boss fight, just like the previous example.
Saturos and Menardi at the beginning of Golden Sun. Its sequel, Golden Sun: The Lost Age had a battle against Agatio and Karst where the plot would progress if you lost, but the battle was not actually hopeless, and winning scored you a nice rare item.
Neclord appears at Warriors' Village and fights the team. He is immune to all attacks and spells, so all you can do is wait for him to kill your team. After your team undertakes a sidequest to a temple to acquire the Star Dragon Sword, you can fight him at his castle and actually win after striking him with Viktor, who wields the SDS for the rest of the game.
The mass battle against Milich Oppenheimer - whatever move you choose to make, he will release poisonous spores and almost wipe out your army of Redshirts in one go, forcing you to break off the attack and go on a quest to find an antidote against the attack.
Suikoden II: You fight Neclord three times, the first two of which are Hopeless Boss Fights. The first time is in the ruins of North Window, before you have the Star Dragon Sword (which you immediately go to get afterwards, but Neclord flees when you confront him in North Window a second time). The second time is in the mines of Tinto, where the hero and his sister Nanami encounter him. In both fights, Neclord is again immune to everything, but instead of having to die, the goal in this game is merely to survive for a few rounds, after which the battle will automatically end. The third fight is a normal boss battle, where he can be killed.
Suikoden IV: Your first fight is against Glen and Katerina, two very hard bosses. They have over 6000 HP each and you only have 4 turns. You either survive the turns or lose, you'll pass. They can't be taken down with a gameshark.
Suikoden V: In an early boss fight that isn't actually that hard if you use some healing items... but, of course, even if you win, the game acts like you lost. This battle is made harder by the fact that you just came off of another boss battle: you may have already spent significant resources against that one.
Suikoden Tierkreis: There are several boss battles where you only have three or four turns to chip away at near-invincible enemies before the plot kicks in again...
Inindo: Way of the Ninja throws this at you as the first battle of the game.
Naturally, the Final Fantasy series has an abundance of examples:
At the very start of Final Fantasy II, you get beaten senseless by a band of Black Knights. Different versions vary, but whether you see a cutscene or not, you're on a path to a battle you can't avoid, can't run from, and can't win.
In Final Fantasy III, you have to fight Bahamut, normally an end-game boss, very early in the game. During this fight, he has 65536 hit points and heals completely at the end of every turn. The player is expected (and encouraged) to run. If you somehow manage to defeat him, though (by using a cheating device, usually) you are actually penalized; you get nothing for that fight, and he no longer appears later in the game, making it impossible to get him as a summon.
Also from the same game, the first battle against the Cloud of Darkness.
Also, early in the game, if the player tries to move too far into the sea without completing a certain task, he will encounter the Dragon Nepto, whose sole purpose is to block the player's path. However, the game ends normally after the party dies and it's impossible to run from him either, forcing the player to reload the game. It is, however, possible to beat him with massive overleveling, but once you do so, you will be moved a few inches back and the boss will still be there, blocking your path.
Final Fantasy IV also featured a weird version of the trope; the Dark Elf seems to be a Hopeless Boss Fight, but once he defeats you, you get the "Game Over" screen. You have to get a special item from Edward in order to fight him normally. If you have said item, the first fight with him is a Hopeless Boss Fight, but then you fight him again as a normal boss.
With sufficient Level Grinding (or by cheating) it is possible to win the majority of the hopeless boss fights in Final Fantasy IV. If you defeat Kain the first time you fight him, the game pretends you lost. If you defeat the Dark Elf without the Twin Harp, it sets the game back to before the battle. The only fights that are unwinnable under any circumstances are those in which a) the player does not have control of the characters, or b) the fight ends regardless of how you're doing.
The sequel has the Mysterious Girl fill this position several times throughout the game. Also, the fights against Dark Cecil and the Mysterious Girl and Bahamut are Hopeless Boss Fights that result in game overs if the player doesn't have the correct party members. Of course, the game doesn't tell you this.
At one point in Final Fantasy VI, the game requires one character to stay in a certain town until they fight a certain character. In this case, the Hopeless Boss Fight Guardian attacks the party if he tries to leave, activating what it calls "Guard Mode". No attacks can damage it, and it counters with a powerful blow — the only option is to run. In the final dungeon, the Guardian attacks again, but this time it activates "Attack Mode" and actively battles the party. By now, most players will gleefully accept the opportunity to destroy it. The Guardian also appears in Vector if you go there when you aren't supposed to. Basically, the Guardian is the Border Patrol subtrope played straight.
There's also another Border Patrol in the same town- the Heavy Armor. You actually can beat this one, as it's just a standard mook from slightly later in the game when you have more characters, but only if you are over-leveled. There is no real reward for doing this, though - the only purpose this enemy placement has is to force you to solve a puzzle segment.
Another example occurs in the second half of the game, when you find Terra in the ruined town of Mobliz. While you're suppose to lose the first time the boss attacks, it's possible to kill the boss by exploiting a glitch with the Useless Useful Spell. The end result doesn't change either way, though.
You can exploit another, lesser known glitch (Echo Screen+Joker Doom) on the Guardian as well.
Final Fantasy VIII features a robot that chases the party during an escape sequence. Every time it catches up with the party, it has to be damaged past a certain threshold causing it to enter "repair mode", which allows the player to flee. It can be defeated for real, but only by abusing its elemental weakness and grinding certain spells. If you do manage to destroy that spider, you get an extremely high score on your SEED combat ranking and a whopping 50 AP bonus (the game's second type of experience), rather than nothing at all happening.
And it's relatively simple to beat if you played cards beforehand to gain some good magic, and then mashed away with Squall and Zell's limit breaks. The only time it's impossible to beat is during the first encounter.
Likewise, the Deling City assassination mission in the same game has a boss that's not hugely tough, but the only difference between winning and losing is that winning gets you 20AP
Final Fantasy IX plays with the trope with the Beatrix battles. It is entirely possible to get a Game Over if she kills everyone present (and she likes to spam Shock, which is a 1-hit kill barring Level Grinding and awesome gear), but you can't defeat her. Once you take out her allotted health pool for the fight, she fires off Shock Break or Climhazard (ironically, both cost less mana and do less damage overall than Shock when she or Steiner use them under the player's control) and reduces everyone to 1 HP before leaving. One useful thing about these fights is that she always has some very nice pieces of equipment for Zidane to steal off of her before she ends the battle.
There also when you fight the game's Big Bad, Kuja. At first it looks like you're going to beat him (prior to fighting him you beat someone that he was confident he couldn't beat), but then he goes into a superform and defeats with his ultimate move.
Final Fantasy X has Geosgaeno, who Tidus first encounters shortly after being transported to Spira. Its physical attack only does percentage-based damage and it has no other attacks, making it seem like a foregone victory - until it tries to inhale Tidus, who then wisely decides it's time to get the hell out of there. Later on, you can fly back to Baaj Temple for a rematch, which this time is winnable.
Early on in Final Fantasy XII the party is attacked by Ba'Gamnan and his crew. If you've been leveling normally, it is extremely difficult to win this fight, and the game makes it clear that you're supposed to run away from them (all the way back out of the dungeon you've been going through.) You fight them again later as a mark. Interestingly, if you've done enough level grinding (or gotten everyone a Quickening), you can beat them here, but you still have to leave the dungeon manually - and the game still shows your guest party member running on ahead of you at each zone transition as though you were running away.
Final Fantasy XIII has a rare case of this and Heads I Win, Tails You Lose in the same fight. Snow fights a bunch of soldiers alone, and although it's quite manageable (and probably easier than the boss battle directly afterwards), you don't get a game over for losing, nor do you get anything of value for winning. Either way, the following cutscene is the same.
Another example comes from Hope taking a level in badass right after Snow practically broke his back saving him. The boss mob you fought not fifteen minutes earlier, with BOTH Hope and Snow fighting fit, comes over and incapacitates Snow. Hope then takes on the boss by himself! There's no way to win this fight alone, though; whether your HP drops to 1 or you fight the boss for an extended amount of time, Lightning and Fang come to the rescue.
Crisis Core ends with one of these: As Zack, the player is forced to fight his way through an unlimited amount of Shinra infantrymen (they will not stop coming, the battle is scripted to end first), who then leave Zack bloody, bruised and barely able to lift his sword at the end. Then three more Soldier infantrymen show up and pump him full of lead, similar to the God Of War II example below (except that he doesn't get better).
Dirge of Cerberus has a fight with Weiss the Immaculate, who initially moves so fast he's nearly impossible to hit. He also takes a VERY small amount of damage, but it may be theoretically possible to beat him. After Vincent is defeated, he gains enough control over his Super-Powered Evil Side to be able to keep up. The following battle is on more even footing.
Dissidia 012. If, at the beginning, you answer that you're a "Dissidia expert," it will make you fight the superboss version of Feral Chaos with your singular preset level 1 character. Overlaps with Trolling Creator, because you're likely trying to avoid unnecessary tutorials because you've played the original, and this doesn't actually prove that you lack knowledge, just the levels and equipment to make winning probable.
This is a real pain if you don't know it's coming (wasting healing items). This is also true in the Japanese version; you always use a Phoenix Down when you get killed, and this boss is no exception. Thankfully, they fixed that.
Seen in Kingdom Hearts Birth By Sleep in Ventus's story when you fight Vanitus for the first time in the badlands, as soon as he is down to one HP the game ends the battle. Later, Micky teams up with Ventus and the fight is winnable.
Many times in Radiata Stories, whose system is such that the bosses secretly have infinite HP but otherwise fight on what appears at first to be equal footing with the player (only doing about as much damage per hit as normal enemies, etc.) However, after hitting the player about 5-10 times, they suddenly unleash a Limit Break that is unavoidable and (on normal playthroughs) invariably powerful enough to wipe out your party in a single shot. With a cheating device (or on a New Game Plus,) the game simply flat-out doesn't care if you're actually able to take the blow and survive—your characters simply fall over and die after being hit with the attack, even if they still have over 3/4 of their health remaining.
Valkyrie Profile gives one either the option of immediately attacking the King of the Vampires, Brahms; or listening to what he has to say. Plot-wise for the Best Ending you should listen to him. Fighting usually results in him kicking your butt and scolding you which results in a decrease in the Karma Meter. However, if you actually beat him, the game just ignores that the battle ever happened (although you do get the karma bonus).
And if you get the "C" ending, Freya comes down and kicks your ass.
The same happens in Covenant of the Plume if you use the plume too much and during two of the endings. For the "A" ending, the initial attack against Garm is unwinnable, and all you have to do when you fight the Valkyrie in the "B" end is reduce her to half (or less) HP.
In Lufia And The Fortress Of Doom, Gades is unbeatable. In following games he is meant to be lost to, but is beatable with some effort and over-leveling. Defeating Gades in combat would result in a rare equipment drop, and a slightly altered cut-scene afterward where the Sinistral blinks, then uses non-combat cutscene powers to defeat your characters anyways.
In the first game, it is truly impossible to defeat the first Sinistral, Gades, when you first meet him (not counting the prologue). It's something of a tradition that this guy defeats you when you first him. Amusingly, this guy is depicted as weaker than others in the next games, but in this game he appears to comparable in power (some people say he's actually the hardest).
LufiaTheLegendReturns has lots of these. The first few battles with Gades, the Ancient Dragon M, the first few battles with Daos...of course, as mentioned above, if you do manage to win a Hopeless Boss Fight, you get a sweet item, then the boss kills you in a cutscene.
At one point during the main storyline of Chrono Trigger, you are unexpectedly pitted against Lavos, the final boss. Defeating him early results in a secret ending that is not canon; unless you've somehow managed to max out the level of all your characters by this point, or are playing a New Game Plus, doing so is nigh impossible. He will surely attack first, and will use a Total Party Kill attack that, assuming you leveled up normally, is instant death. You'll barely survive it at a decent level. To drive the point home, this iteration is actually even more powerful than the "standard" final boss; he hits harder and attacks faster than normal, just to make sure you lose. Disappointingly, even if you win, you don't get to see Queen Zeal's reaction to the "invincible" Lavos being defeated right in front of her.
In the Kingdom of Zeal, the plot requires you to be captured. To this end, a Golem is sent to attack the party. While the standard fare would be to lose to the monster, you can actually defeat it (in fact it can be pathetically easy if you know how). Doing so results in the summoner using the "look behind you" trick then shooting you in the back. All winning does is net some decent EXP. What's worse is that, later on, the same guy will summon two of these things that you are expected to defeat, so unless you figured out how the first time around, good luck.
If you go to the Northern Ruins in 1000 AD, you'll encounter Cyrus' ghost. Physical attacks always miss on him, and he's immune to all elements so magic doesn't work either. The battle ends automatically after a few rounds with the party realizing they can't beat him. The correct thing to do here is to go to the same area in 600 AD and Set Right What Once Went Wrong.
In the sequel, Chrono Cross, the main antagonist switches bodies with the player character in the middle of a fight. The resulting battle cannot be won: either the player character is beaten down by his former allies or (if he manages to beat them), one of the stricken characters drags herself up and stabs him before collapsing again.
Similarly, the two Big Bads in Skies Of Arcadia, Galcian and Ramirez, have infinite HP if fought at any point besides their final appearances. Annoying because both would be relatively easy bosses without this feature.
Also, the Red Gigas is completely invincible when you fight him, forcing you to just survive until a scripted event. The Green Gigas does have a limited life bar, but such a ridiculously high HP count that the game expects you to immobilize him instead. However, neither fight actually requires that you lose, making these a borderline case.
The Red Gigas does in fact take damage; it's just that he has such ludicrously high HP that after multiple Harpoon Cannons and combination attacks using torpedoes, subcannons, AND main cannons, he's taken just enough damage to his health that the difference is actually visible. Similarly, there is an odd glitch when facing the Green Gigas the first time, which prevented the immobilization from taking place, and as such had to knock his HP to zero to kill him. The immobilization cutscene occurred anyway.
Ramirez can be fought if you either cheat or overlevel. If you're strong enough to withstand his ultimate attack (which after a while he starts spamming over and over again), and are willing to spend several hours fight him, you can get his HP down to 25%.... whereby the game glitches up and goes to the cutscene where you lost. Talk about hopeless. Ironically, if he had his final boss stats (where he's supposedly stronger, storywise), he probably wouldn't even be that hard to beat.
Ramirez has 9.999.999 HP in those unwinnable battles. Worse, in the first battle against him in Nasrad he can cast Sacrulen (a FULL HEAL on himself) if you hack the game to reduce his HP.
In Tales Of Destiny, Leon is nearly impossible to beat the first time you face him, which is quite early in the game. If you do manage to win, you get a special ending right then without playing through most of the game.
In the PS2 remake, however, your efforts are rewarded by him suddenly unleashing his Limit Break and ending the battle regardless of whether everyone actually got KO'd or not.
The first fight against Shizel in Tales Of Eternia. She'll give you the illusion that you're actually fighting her, and after a little while, she opens up a can of god-power that knocks everyone down to 1 HP before effectively flicking everyone to death. (Bonus points if, instead, the A.I. Roulette decides to finish you off with something powerful like Prism Flasher.) If you manage to pull yourself back from the brink of defeat, the game cuts away from the battle abruptly and pretends you lost anyway when she's reduced to half HP.
You can actually avoid losing the first fight against Yggdrasil (though that isn't likely because if you lose the scripted fight prior to that you will start the fight off with 1 HP), but it is virtually impossible to beat him because the fight will automatically end after a certain amount of time. However, using certain New Game Plus upgrades, you can win the fight and force him to flee. He then pulls out Cutscene Power to the Max, giving you a glimpse of his nifty Sword of Plot Advancement in the process, which justifies both the trope and the rescue cutscene immediately afterward.
The first battle with Vidarr has a feeling of this trope included as well. Although you still have to win, no matter how well you do, your team will get a cutscene with them about to be killed, only to be saved by Kratos. You can Action Replay this, hit him once down to near death, but this scene will trigger regardless.
The party's first battle against Vaclav in Tales Of Legendia. He only has about 8000 HP, but once you've worked him down to about 4000 he unleashes a massive spell that knocks your entire party unconscious.
Tales Of Legendia flat out spams this trope. You get stuck with unwinnable fights in chapter 1, chapter 3, chapter 5, and twice in the last chapter of the black mist story arc.
Funny thing about the unwinnable fights in Legendia, is that the fights you are supposed to lose, is that the attacks the boss "defeats" you with actually do 0 damage.
Tales Of Hearts features two boss fights you're "supposed" to lose, the one against Chalcedny early on for Kohak's Shy Spirune and the one against Sorceress Incarose about halfway into the game. Both of them are technically winnable, and in a subversion, if you beat Chalcedny, he actually does hand over the Spirune immediately (though the party finds another excuse to go through the area where you'd normally actually get it back).
Symphonia's sequel, Dawn of the New World, has so many of these, that the player may have trouble discerning whether a given boss battle is winnable or not (on his or her first playthrough anyway).
The game also has two types of these: Fights that are just really, really hard to win, and fights that you can't win at all (because the boss' HP won't go down). This can become downright ridiculous, like the first fight against Commander Brute. Cue a long string of "Impressive !" as he flinches constantly under your attacks... without losing any HP. During the second encounter, he doesn't get any stat buff but loses that plot invincibility. Curb-Stomp Battleensues.
Lloyd, the first boss of the game is normally unbeatable, but if you can carry your strongest monsters over to your second playthrough, he's somewhat beatable, thus netting you at least 10 levels of experience. But the story advances as if you lost.
Tales Of The Abyss has a fight where Luke fights Asch alone that is expected to have you lose. You can win, but it requires you to be either very skillful with the battle system, level grind, be in New Game Plus, or have a lot of healing items. There is a slight variation in the cutscene after if you do manage to win, and you do get experience, so it's not all for nothing at least.
It's pretty entertaining to hear Asch whine and cry about how worthless he is because he just lost to his replica.
Not really related, unlike other scripted fights in the series, the scripted boss enemy is actually weaker the bad guys he's supposed to equal in rank, but it evens out since you fight him with only one character.
The original version of Tales Of Vesperia didn't have one of these, but the PS3 version adds a one-on-one fight between Yuri and Don Whitehorse at the end of Keiv Moc. It is possible to defeat him, even on the first playthrough...but only if you've undergone some serious Level Grinding, set the difficulty to Easy, and are very, very dedicated - otherwise, you'd be best advised to try again the second time around. Nothing changes much if you do win except for acquiring an okay-but-not-great accessory (a Diamond).
In Tales Of Graces, the first fight against Hubert in the adult arc is this. Even if you're either leveled enough to deal decent damage against him, or skilled enough with the game's combat system to dodge his very wide close-range attacks, he'll build up his eleth gauge incredibly quickly and then use his Mystic Arte to end the battle.
Unusual example from Baldur's Gate: At the very beginning of the first game, as you flee the training area of Candlekeep, you and NPC Gorion are accosted by an armored figure who will eventually be Sarevok, the final boss of the game. A cutscene follows in which the PC flees and Gorion engages the enemy and gets himself killed. However, the battle is still conducted according to the regular rules of the game engine, and occasionally Sarevok's final swing actually misses — but because the game is scripted that way, Gorion drops dead regardless.
If you manage to make Gorion or Elminster hostile to you, you won't live long; their battle scripts makes them cast one Lightning Bolt spell for show and then just executes the kill() instruction on your main character, which is Exactly What It Says on the Tin: an unavoidable One-Hit Kill.
In Baldur's Gate 2, you're not even given the option to fight; many boss characters will simply automatic kill you if you advance the plot wrongly. Those that can hit obviously have infinite life points. You can kill them by using an exploit but that would often times prevents you from advancing the plot.
They did not have infinite hit points. Rather, they all wore a secret belt that simply prevents their hp from falling lower than 1. You can see this belt right at the start of the game, when Imoen is wearing it. As Imoen is essential to the plot later on, she cannot be killed; if she were to fall below one hit point, a script causes her to panic and run away. The exploit that allowed you to kill essential characters was that if you somehow managed to reduce your constitution or intelligence stats to 0, you would die regardless of the hitpoints you had. The ability to reduce constitution only shows up in a few traps and is inaccessible to players, while the ability to reduce intelligence shows up in the game for only a short time; The mindflayers you encounter in the underdark automatically do this on a successful strike (hint: they're eating your brains). There was one item near the endgame that allowed you to summon/transform into a mindflayer for a short time, thus allowing you to reduce intelligence.
That exploit was fixed in the expansion, though you probably wouldn't have access to it early in the game without cheating anyways.
In Mega Man Battle Network 3, Bass is completely unbeatable the first time you fight him. He has a shield up that prevents the main character from ever doing any damage. It can even block a chip that's sole purpose is to blow away those kind of shields. It was found that, through an attack combo, one could damage him through this shield, but it does no good. He won't be defeated even if his health drops to 0. Naturally, this shield has become his usual 100-HP aura in time for the real fight (with no plot explanation given).
There's a bit of an explanation for the shield turning to usual, actually. Bass had just absorbed part of Alpha's program, which actually weakened him and probably caused his aura to become not-invincible.
Similarly, you can't do anything to ShadeMan in MMBN4 until the second go-round — and even there, you have to let him beat you up a bit.
MMBN1 presented an unbeatable ElecMan, who recovers completely from all major damage and also won't be defeated even if a player is quick enough to drop him to 0 HP. Rather than dying, however, you only need to watch ElecMan heal himself a few times before the heroes learn they need to disable his power and begin the real fight.
While we are talking about Mega Man, we should mention Mega Man Star Force which has four bosses that are unbeatable.
After you beat HarpNote in the first game Geo is tricked by Luna Platz to coming back to school by having him look at the play set (which is about the battle against Taurus Fire) a jammer drops a light on you but misses, after which you have to chase after it. When you finally catch up with it, the jammer ambushes you, you battle and then after 4 turns the battle ends and he strangles you causing your character (Mega Man Geo-Omega) to pass out and un transform.
Then in the second game you go to the shopping center area (where you battled Dark Phantom and later on battled a eyeball monster), while here you are forced by Hollow to save people from multi colored knight monsters. After you beat them you are forced into a 4 round battle against Solo-Rogue after which Sonia shows up and saves you.
Next in the third game, you first have to go up against J Corvus, after 4 rounds the battle ends and Joker shows up and datafies Luna. Then later on you have to go up Acid Ace who has been corrupted by Joker (who else?) and after a 4 round battle (what else?) the battle ends and he un transforms and collapses on the floor of the concert stage at the TV studio.
The battle with Queen Beryl in Sailor Moon Another Story. Her regular form is perfectly beatable, but upon defeat she transforms into Super Beryl, forcing you to fight her again, twice. During the first battle in that form she has a move that does 9999 damage to each character in your party regardless of their stats, and she almost always uses it on the first turn, sparing you from futile attempts to defeat her.
Romancing Sa Ga had this with the Diamond Fatestone, it is possible to win, but very hard considering your levels at the time you talk to Schiele the final time, especially on New Game Plus where even after talking to her once after clearing the event in prior playthroughs, the event will trigger.
Breath Of Fire III has two bosses, Balio and Sunder, who are fought twice before you can actually beat them. It is possible to temporarily hold them off in the second fight, but the first is completely unwinnable. It was years, though, until this was completely proven. A rumor, fueled by a strategy guide misprint, insisted that there was a prize for winning the fight even though this is impossible.
It was eventually found that they don't even have HP values in the first fight - they're just targets you can hit. It's actually possible to lock them in an infinite loop of trying to cast a spell without enough MP and attacking each other.
There's also Garr in the Inevitable Tournament. If you stall too long, he says "Let's finish this!" and defeats Ryu with a super critical.
There's also a few in Breath Of Fire II. The very first battle of the game, the second battle of the game (against a giant, vicious demon that later returns as the second-to-last boss, no less) and the optional fight against Tiga late in the game. The first two can be excused, since you're in control of a small child (Ryu can't be much older than 8 at that point, as he seems to be a teenager, 10 years after the fights), but how Tiga manages to keep going is a mystery, especially since he's later CurbStomped by a boss that isn't even that strong.
This is reversed in Breath Of Fire IV You instead play the Boss and he is so powerful you can't lose even if you try. You play him so he may not be considered a boss but he still fits, in every other way, the typical role of the last boss. If you beat him by using a cheat device, the game freezes.
Right before you fight the final boss, you have a scripted fight with him where he will eventually defeat with an instant death move.
In Grandia, your first battle with Gadwin is a Hopeless Boss Fight, as he takes no damage from any attack, and will eventually attack you with Dragon Cut, which will deal 9999 damage.
The first time you meet Millenia in Grandia II is a Hopeless Boss Fight, as she has infinite health, and the fight only ends when she blasts your group with a lightning spell. Notoriously, this fight can glitch and go on indefinitely with her never casting the spell that ends the fight. This is repeated for a few other battles; it is particularly noticeable in this game because Grandia 2 has a mechanic that normally would allow you to prevent enemies from acting by interrupting their attacks. Naturally, this wouldn't do in an unwinnable boss fight, so instead all such attacks simply and inexplicably fail, the only point in the entire game at which they do so. When you fight the same bosses later—sometimes only shortly afterwards, with no explanation for the change in power or winnability—your attacks start working as normal again.
This sequence of events differs very slightly in the Dreamcast version of the game; Using a cheating device to increase Ryudo's health, speed, and damage potential means the battle can be won by reducing Millenia's HP to 0 - though this is incredibly time-consuming and if she is able to use the lightning spell mentioned, the fight will end immediately. Your counter move also functions as expected if you can land it at the right time. You don't gain any rewards for winning this way, and the game continues as if you'd lost to the lightning spell anyway.
In Jade Cocoon: Story of Tamamayu, when the main character fights the Dream Man and his dragon-like minion in his dream, he cannot be defeated. Even if you win (through cheating or pure luck), only the dialogue changes during the scene after the battle, with the main character still lying on the ground as if defeated.
You can win by regular methods as well. He's difficult, yeah, and definitely this trope. But precision tactics can defeat him.
In Jade Cocoon 2, towards the end of the training forest, the main character touches Nico's cocoon and is cursed. The subsequent battle cannot be won without cheating, since the Kalma the main character must fight is too powerful for your two newly hatched Divine Beasts to handle. After your inevitable defeat, the main character is "possessed" by the Kalma. However, you take him on a second time much later in the game, and while he is definitely a challenging opponent, he's far from unbeatable.
In the first SaGa game (Final Fantasy Legend in the US), three of the worlds feature demons whose appearance signals the end of that world's plot. On the fourth level, however, the level boss Su-Zaku attacks pretty much constantly — but he's immune to (almost) all possible attacks. After you develop the weapon to defeat his shield, he becomes frustratingly less ubiquitous and has to be tracked down. Oddly, due to a bug in the combat code, he is not in fact invulnerable to all attacks in previous encounters; the Saw instant-death weapon (which is a Game Breaker due to a programming error) can defeat the otherwise invulnerable Su-Zaku, but doing so does not prevent his reappearance or advance the plot in any way.
In addition, a character with high enough stats will have no problem slicing through his 255 defense.
In Saga Frontier 2, Wil Knight's team has to run away from a human transformed into a giant beast; this battle is unwinnable regardless of how much level grinding you do. (You can, however, challenge it again if you so choose.)
In an earlier chapter, Wil's team fights against two dragons which will kill you under normal conditions, then one of your allies will get back up and commit a Heroic Sacrifice, killing the two dragons and healing the party. If you don't have that specific ally in your party, you lose the fight for good.
In Saga Frontier, the first fight of Red's game, against Shuzer, requires you to get pummeled into the dirt, so Alkarl can show up to save the day.
The old game Might and Magic II had a monster called the MegaDragon in a location reached by Time Travel. It was undefeatable because it served a plot purpose; however, it could in fact be defeated with high level characters and non-elemental spells like Mass Distortion and Implosion. The monster showed up in weaker forms in later games in the series.
In Might and Magic V, there is another unbeatable boss, the Big Bad. Notably, it's not even a fight... if you enter the Big Bad's room without the Big Good in your party, BB eradicates your entire party with a wave of his hand and then you get a game over. If you do, the game goes straight to the ending cutscene of the two of them fighting it out while your party waits outside.
There's a Hopeless Boss Fight in Phantasy Star IV; if you insult it by acting greedy instead of heroic, but you can beat it with enough Game Genie-ing, though you lose the spell you should have gotten from it in the process.
A similar situation occurs in Phantasy Star II. If you kill the security robots coming to arrest you by cheating, Script Breaking happens and you can't progress through the plot.
The original Phantasy Star has what initially seems to be a Hopeless Boss Fight with the "Saccubus", a monster that appears once you fall asleep in the Governer's Mansion and quickly decimates your party at normal levels. Fortunately, it was All Just a Dream. With a bit of Level Grinding, however, it's entirely possible to take down the Saccubus - earning the reward of one single meseta.
The true Hopeless Boss Fight of Phantasy Star IV is actually against Zio the Black Magician, who cannot be defeated due to his Magic Barrier, although further into the game you collect an item that will disable the barrier.
Also in Phantasy Star IV are the carnivorous trees on Dezolis, which are used to block progress until you have the Eclipse Torch. They are unbeatable in that they will continually respawn forever. When they are approached with the Eclipse Torch in your inventory, though, they are instantly destroyed, without a fight.
Wild ARMs: Alter Code F has strange Hopeless Boss Fights. After a few turns, the battle automatically ends — either just closing, or with your party being instantly wiped out — but you still get EXP from the encounter based on how much damage you managed to deal first, so it's still a good idea to go all out.
The Clumsy Robot guarding Monotoli's office in EarthBound makes you think it's kind of a hopeless fight in that it repeatedly eats a sandwich which the game says fully restores its health. The sandwich actually does nothing at all.
Which actually happens after enough damage has been done to the boss—damage that can be dealt with one Multi Bottle Rocket, ending the fight in the first round.
Master Eddy in Mother 3. He uses the last of his strength to generate a whirlpool inflicting mortal damage to your party and wash your items away. You must defeat him to allow him to use his final attack. You just don't gain experience from battle.
Straight after this particular battle you wash up on a beach with all your items gone, and all your characters at a mere 1 HP and 0 MP. Healing your party is impossible without eating from the nearby patch of hallucinogenic mushrooms (an important plot point for this chapter), and there's an enemy Zombieshroom blocking your path forward which, in your party's current state, is suicide to encounter and should be impossible to defeat. If, by savestate-hacking yourself to recovery, you manage to defeat the Zombieshroom without having eaten the mushrooms first, the Zombieshroom simply reappears after battle to block your path again.
The trope is averted in the battle against Porky. When you reduce his HP to zero, he gets into a capsule that makes him completely immune to any attack you throw at him, making it look like you are about to be crushed in battle. However, the boss also lacks any attacks of his own and after a few rounds, the party decides nothing can be done against him and he can't do anything to them, so they just stop fighting and move on.
Early in Legaia 2: Duel Saga, there is a boss fight that pits the lone main character against a brother and sister, both boss-strength. The battle ends when the player loses and the bosses execute an ultimate team attack. Alternatively, a prudent player can actually defeat one of the bosses, at which point they get angry and get right to the team attack anyway. The team attack doesn't do damage, it just ends the boss fight.
Two dungeons earlier in the game is the battle against The Man With Golden Eyes. He takes zero damage from attacks, and simply watches you until you've attacked several times, then easily defeats you.
An aversion is the battle against the Blue Knight while trying to escape from the castle early in the game. It's a timed battle, and he's very strong, so that it seems like you'll lose if you take too long, but you can't win if you rush him. The timed battle aspect is false: no matter how long you take to kill him, you'll win.
In Knights of the Old Republic, players can trigger an optional Hopeless Boss Fight by pissing off Calo Nord in the Lower City cantina on Taris; since the plot requires his survival, he's invincible here.
For that matter, the nameless Sith mook running the sentry turrets at the elevator from the Lower City to the Undercity? Likewise invincible! Trust me, never choose the 'fight it out' option in the dialogue. Those sentry turrets just don't stop.
In your first encounter with Darth Bandon while escaping the Endar Spire, the fight is so hopeless that you don't even get to try. Your Red Shirt teammate sacrifices himself so that you can escape.
In your first duel with Malak, you can't kill him. You can only hold him off until Bastila shows up and sacrifices herself to let you escape.
Doubles as a poorly implemented example of this trope: Malak is incredibly weak in this appearance, is easily bested and actually flees at one point before Bastila "sacrifices" herself to buy you time to escape, massively lessening the impact of said sacrifice in the process. Doubly irritating since in his Final Boss form, he's way more difficult.
In Knights of the Old Republic II, Darth Sion literally can't be killed. Every time you reach a damage threshold, he becomes invincible for a moment as his health is restored. With the right build, you can keep him on the ropes forever, but pure combat won't ever work. When you meet him on Korriban, Kreia makes you and your party run like hell after a few hits. The second time, you have to talk him to death.
In the Expansion PackShadows of Undrentide, you are expected to do a couple of quests in the Elven Crypts for the spirit of an elven hero. If you complain even once about this (something fairly innocuous along the lines of "Oh great, more fighting...", when rebutting other characters in much stronger terms just scold you before carrying on), he takes mortal offense and attacks you. At the level you're expected to be at (around three at most), you will die.
In the Tournament of Arms, should Claude make it to the final match (he does not have to, but you get a decent weapon that can be upgraded into Claude's ultimate weapon if you do, so it's well worth the effort), he will face Dias Flac in a Hopeless Boss Fight. Dias is invincible here and will take off a set percentage of Claude's HP with each strike, meaning you'll die in a few attacks no matter how strong you are. It should be noted that, with the help of a Game Shark to put attack items in your inventory (all your items are temporarily taken from you before the tournament begins), you can actually defeat Dias, but storywise, the game will still consider you to have lost the fight.
Dias cannot be beaten. You can 'shark Claude to have 9999 STR and CON in one playthrough. Every monster in the game, including the final boss and all the optional bosses, did zero damage to him, and Claude in turn always hit for 9999 regardless of what weapon he had. Dias... two shotted Claude. Dias either took zero damage or outright blocked every one of Claude's attacks. If you include the above poster's cheating in attack items, only the Magic Rock will damage him, but his HP never decreases. That's what makes him Unwinnable by Design.
You actually CAN defeat Dias, sort of... As it turns out, Dias is invincible, but only until the exact moment Claude is knocked out. If you are strong enough and manage to perform an attack just as you die (perhaps Air Slash), you can force a tie. Of course, since you're dead too, it counts as his win. To summarize, just take the consolation prize.
At the Lacour Front Line, you'll face a monster called Shin that is also immune to all attacks. The goal is simply to keep your team alive for about one full minute. Afterwards, the fight will end automatically. A short time later, you'll face Shin again, and he is again invincible. The only difference is that to proceed with the game, you have to let him kill you this time.
At the end of the first disc, you'll meet a group called the Ten Wise Men, and face one of them, called Berle, in battle. This is like the first encounter with Shin (who will ironically be finally beaten in the same area you fight Berle in), in that Berle is invincible, and the battle will automatically end after one minute.
Sometime in the second disc, you'll face another of the Ten Wise Men, Marsilio, who is, like Berle, invincible. This fight is like the second encounter with Shin, where you must let him kill you entire team to proceed.
Finally, in the optional Cave of Trials, you'll encounter a monster called the Weirdbeast on the fifth level. This monster is a Hopeless Boss Fight at first, unable to be killed by your team. To proceed with the dungeon, you must run from the fight, and explore the rest of the floor until you find a weapon called the Weird Slayer. True to its name, the Weird Slayer will destroy the Weirdbeast in a single blow (as well as any other creature with the word Weird in its name). The first Weird Beast fight is technically not hopeless, but the Weird Beast only every takes 1 damage from an attack and has over 800,000 HP. You can kill it with the "Medusa Shield" and "Bubbly Potion" and such are all legitimate since they were used the way they were meant to be used. Either way, they are still fairly difficult to pull off.
Magna Carta mostly avoids this trope; there are a number of ostensibly unwinnable fights throughout the game versus powerful boss enemies which you end up having to beat later, but unlike most such games these fights are actually winnable - it just requires a great deal of strategy (and sometimes some power levelling) to do so. Frustratingly, there IS a single truly hopeless boss fight towards the end of the game, one which you cannot win under any circumstances, though it is fairly obvious that it is hopeless... other than the fact that the other boss fights in the game were winnable.
The first Kingdom Hearts features a fight with Leon early on in Traverse Town where you're supposed to get knocked out. It's in theory possible to defeat him, but only through extensive Level Grinding. In Expert mode, the challenge of the fight is just landing a good solid hit on him once before he knocks you out.
Leon isn't actually too terribly hard to fight, even if the player hasn't level grinded. This editor beat Leon the first time ever playing the game. The trick is to time attacks properly and run away the rest of the time. True to form, however, Sora gets incredibly exhausted from the fight and passes out, while Leon seems none the worse for wear (despite his defeat quote of "No way...I can't lose!"). This really isn't worth it, however, as the only reward is some extra XP that can be easily gained later, and an Elixir from Leon later. Still, the satisfaction of Leon admitting that a kid with no battle experience beat him is hilarious.
The trick, much like with Xaldin in the second game, is that you're not meant to just button mash your way through the fight. Even landing a full combo on him results in him immediately smacking you in the face afterwards before you can even recover from your attacks. You're supposed to wait until he jumps towards you, then run under him, and combo him from behind, in which case the last hit will send him flying far away from you, giving you ample stun time to run away. And it's very much possible to do with without the extensive Level Grinding.
Later on in the game, Cloud in the Olympus Coliseum is likewise quite tough to beat, but win or lose, you still go on.
That Cloud is quite easy provided you have cure and guard. It goes either way but you get a lot of experience.
In Kingdom Hearts II, any battles where Roxas fights Nobodies without a keyblade count, similarly to Sora attempting to fight Heartless during the Islands' destruction (again, without a keyblade) in the first game.
Also the first time you face Hades, he's fully invincible because he's the god of the Underworld you're in. You get a second chance later on once you've got the Olympus Stone.
358/2 Days has its share. A battle with a boss heartless who turns out to be Xion under an illusion ends after you chip its HP down far enough, and another battle ends after a certain amount of time has passed.
Wandering Hamster has this trope in the form of Ghost Broaste, who you cannot kill until you find the worthless weapon, his old Teddy-Bear.
In the Magic Knight Rayearth SNES RPG: the first battle against Lafarga, and the first battle against Emeraude.
If you attempt to attack the Big Bad Rhapthorne in Dragon Quest VIII after he's put up his barrier, nothing will touch him, but his attacks will still hurt a lot. To take down the barrier is rather involved, requiring a side quest and a complex ceremony - in the middle of a battle.
The first encounter with Marquis de Leon (Keeleon in the American version) in Dragon Quest IV also counts, since after defeating Balzack, he's powerful enough to easily One-Hit Kill Meena (Nara) and Maya (Mara) before they can even put a dent in him. The battle will end if both of the sisters are knocked out, regardless of how much health Oojam (Orin) has.
The fights with Reaper Beat and the Trance Rhino (a Taboo Noise) may feel hopeless the first time through, but cut off after a certain amount of time regardless of who's winning. But if you die before that, the Game Over is for real.
The battle against Taboo Minamimoto feels hopeless as well, as it typically ends with your defeat. However, if you are defeated too quickly, you receive a Game Over instead of the cutscene that follows.
In a New Game Plus, both Reaper Beat and Taboo Minamimoto appear as Blue Noise symbols and can be fought in optional, standard battles.
And you'll probably fight them over and over. If not for the satisfaction for kicking their asses, then for the sweet pins they drop that you'll need for some of the more useful stickers.
The first boss fight in Metal Max Returns is an unusual version of this. The enemy is far too powerful for you to beat as early in the game as you fight it... but you lose as usual if you die. Instead, if you manage to survive for two rounds, a computer-controlled character joins the fight and will win it for you on the next round; you still get the reward for winning, but it does have some consequences in the plot.
Xenogears has Id and his invincible Gear show up to beat the party into the ground a couple times.
Followed closely by an impromptu fighting test culminating in a Hopeless Boss Fight against eventual party member Rico.
In the most famous fight about Id, you can win (the other fights aren't exactly a loss). Plot-wise, you still lose. Against Rico though, I don't care what you say, you cannot win that fight without Gameshark.
And even if you do use a Gameshark, you still can't win. After beating down Rico (which takes a while - he has about 65,535 HP, give or take) the game simply continues as if you'd lost!
Alpha Weltall is a boss you aren't supposed to beat either, but some crafty and Crazy-Prepared players have beaten him, and do so as a sport.
Alpha Weltall doesn't really require any special, specific tactics or equipment to defeat. A player who understands that Magnetic Coats and Ether Doublers turn your Gears into nigh-invulnerable mini-gods have probably been using them for most of the game anyway.
Since it does have a drop if you have the Trader's Card (The "Slayer's Robe") it seems the writers had some idea it was possible.
Quite a few of these show up in Xenoblade Chronicles, and they'll end if everyone gets KO'd, a certain amount of time passes, or if you cause enough damage to the boss. In the latter two situations, the boss will simply send everyone flying with a special attack to end the fight. Their HP also simply stops decreasing once it reaches the "You lose" threshold, so you can't win even on a New Game Plus, where you could realistically OHKO some of them otherwise.
A truly interesting example that's impossible even on a New-Game Plus! Your first encounter with Morag in Magi-Nation begins like a normal boss fight, with Morag summoning one comparably weak Koil and doing nothing else until it rolls over. After that he gets mean and continually summons Borgors until they eventually slaughter you. Not only are the first few incredibly over leveled at this point, replacement Borgors (which you flat out will NOT see on your first playthrough because the first ones are so damn tough) are even higher in level, and Morag has 65 million energy, compared to the second-highest boss with roughly 1500 (who is not the final boss by the way). Later on you have a normal boss fight with Morag who is incredibly weaker, with only a few hundred energy, but has more variety to his monsters and also casts spells.
In Ys VI: The Ark of Napishtim, the secret room that contains the Eldian Orb, which is a Guide Dang It to reach, is guarded by a innocent-looking goldfish-type miniboss called Majunun. Unless you really max out your experience(which takes forever, since in the higher levels all enemies only give 1 EXP), you have no chance at defeating it. In fact, its attacks will One-Hit Kill you at the level you are at when you can first reach the room.
And in the remake of Ys III, Oath in Felghana, the first battle with Nicholas Garland is unwinnable. His shield simply cannot be broken, no matter how much damage you pile on it. The only option is losing. Of course, the second fight is perfectly winnable.
Also, in Ys IV: The Dawn of Ys, Keith Fact is possessed and turned against you, and the only way to proceed is to be beaten.
Rentar-Ihrno in Spiderweb Software's Avernum 3 cannot be defeated in the final boss battle. This is not so much a hopeless battle, however, as the objective is to disable their doomsday machine.
Players who've managed to handle her with Wall of Blades spam report that nothing happens when she falls. You just go and turn off the machine anyways, and the ending progresses as normal. At least Spiderweb learned their lesson for the fourth game—the Shades regenerate to full health every turn, making their defeat mathematically impossible without the necessary weapon.
In Persona 4, the fight with Shadow Rise mixes this with Bait-and-Switch Boss. Halfway through the fight, Shadow Rise begins to "scan" your party, becoming immune to all your attacks in the process. Teddie unleashes a Desperation Attack to save you, leading to Rise acquiring her Persona. It then becomes apparent that the actual boss in this dungeon is really Shadow Teddie.
The final boss of Persona 4 pulls this twice. Ironically, your Eleventh Hour Superpower then turns you into one for them. A harsher example is the final boss of Persona 3: even though you become immune to the One-Hit Kill, the only way to stop Nyx is to sacrifice yourself. To be fair, you technically win...
Somewhere between Hopeless Boss Fight and Heads I Win, Tails You Lose, but closer to this one: The first battles with the Gizoid Centurions and Prefect Charyb in Chapter 10 of Sonic Chronicles: The Dark Brotherhood. The party is split up into two, and after one team starts to take on these almost invincible bosses, you get a cut scene of losing after three turns of survival (losing in the first three turns gets you a standard Game Over). After this, the action cuts back to the other team, which does something to neutralize the enemy's Nigh Invulnerability shields. You want to focus on restoring your own health and PP, though, because when the battle resumes, you'll be at whatever status you were at the end of the previous battle.
And very soon thereafter, you have the first encounter with Fox Face. And all subsequent encounters, really: Fox Face is unstoppable, and you have to run away from him. Even when you do finally manage to defeat Fox Face, he's replaced with the four masks of malice, who are likewise unstoppable until a certain point.
This happens several times in Wild Arms 5. The game doesn't even pretend to be fair during these battles: any attacks against your opponent automatically fail (with an explict "No Effect!" message) and analysing the enemy reveals that you gain no experience points for a victory.
While the first 'unbeatable' bosses are impossible to defeat, the rest of them can be beaten as long as you're not a one-man party, have a lot of revive items, and most of all, the ability to unleash finest arts (equipping a punching glove on a character with the Sword medium equipped, thus activating finest arts whenever he uses 'Sonic Vision'). Luck helps, too. Furthermore, you do gain a lot of experience points from the victory. Some examples of these fights are the first Golem the human characters fight or the first battle with the Ice Queen. However, the following cutscenes remain unchanged.
A variation occurs in Valkyria Chronicles on the first two occasions where you fight Selvaria. In the first case she's utterly indestructible, but if you just ignore her (and take loads of cover from her gatling laser) you can still complete the objective, and in the second she appears a long way from the main objective but spends her time casually blowing up your tanks and causing instant mission failure.
That second one doesn't really count - all you need to do is pop the Edelweiss out of a hole, hit her with a mortar shell, and duck the tank back into the hole. In practice, the only thing this does is to cancel out the extra moves you get by having the tanks on the field in the first place. However, if any infantry units are in the wrong place when she shows up, it rapidly becomes hopeless for them.
In a reversal, Alicia takes on Valkyria powers eventually and becomes this for the imperials, utterly ignoring gunfire while running around smashing everything she comes across
In Valkyria Chronicles III, the final fight against Dahau it's impossible to even scratch him, something he attributes to 'the force of destiny' (a pretty big theme amongst the Darscssen, including two of your party members). The real objective of the mission is to destroy the ancient superweapon he's going to use to set the world on fire.
In Radiata Stories, the first battle (against Ridley Silverlake) is deliberately rigged for you to lose. Your attacks are woefully underpowered, while she can deal double digit damage per attack. Even if you manage to avoid getting your HP axed to zero after about one minute, Ridley will pull off her Wild Pitch special attack that instantly knocks you out, no matter how high your HP is.
In Pokemon Ranger: Shadows of Almia, the fight against Darkrai is like this until your Capture Styler gets upgraded.
In the PC version of the famous D&D adventure Temple Of Elemental Evil, an evil god by the name of Iuz will suddenly join a battle which your party would've (by this stage of the game) been able to win reasonably well. Iuz has a VERY large number of hit points, and can easily kill a healthy barbarian in a couple of strikes. The idea is to try to avoid getting your entire team slaughtered (which can happen very quickly), until a couple of turns later another god shows up. At this point, everyone in the team is resurrected, as are the enemies, the two gods disappear, and the whole fight starts over from scratch. In other words, you're expected to try to survive for as long as you can. Surprisingly, there are actually people who've defeated the god, and the designers even added an extra "achievement" reward which is acknowledged in the endgame slideshow. Good luck though, it is extremely difficult.
In Lost Odyssey, the end of Disc 2 pits the team against Councilor Gongara. After he taunts them for several turns about how pathetically weak and ignorant they are, he wipes them out with a single spell.
In Digital Devil Saga, there's the Jailer, a Horse like demon that is scary as hell. until you weaken him by replacing his normal supply of canned fifteen year old with rotten meat. He'll use Black Bind which renders the party immobile and ends the battle.
Azoth of Destiny also has the first encounter with the Dragon King, Ardgevald. To say that Ardgevald annihilates you is a massive understatement: he unloads three immensely powerful attacks before you even get to think about moving, the third one doing overkill damage just in case the first two didn't beat you all the way to death yet, and the battle ends right there and then with your party flattened on the ground. You later on get to fight him for real after getting stronger, and while the battle is winnable, he still does enormous damage and can very easily curbstomp you again, showing that his earlier stomping of your carcass wasn't all plot power, but him being legitimately tough.
Near the end of Fossil Fighters you have to face the police chiefwho's actually the boss of the criminal organization you've been facing. His dinosaur that he summons has max evasion so every attack you throw at it will miss. Though it isn't superpowered the fact that you can't hit it makes it a Hopeless Boss Fight.
In The Elder Scrolls IV Oblivion, it's not technically a boss fight but one of the optional daedra prince quests requires you to anger a widower and let him attack you with a special blade. The only way to win the quest is to die.
Dragon Fable's Fire War kicks off with a Hopeless Boss Fight against Akriloth, which sets off the Start of Darkness for Drakonnan. Some battles against Drakath also qualify, as does Xan, Sepulchure, and several more.
Also in Video Game/Dragonfable, it is possible to beat the Elemental Lords as Nythera rather than as Warlic. You get quite a chunk of experience, but the battle is retconned and you have to do it over. Strangely, the battle is a lot easier as Nythera.
In the Dragon Fable minigame Archknight, there's a boss you meet at level six or seven who has more than thrice your HP. Naturally, it's this trope and critical to the plot.
Two in Last Scenario. One, the first fight against Felgorn, is a true Hopeless Boss Fight, as as soon as you get him down to half his hit points, he hits you with a Total Party Kill attack. The second is more to show The Hero's Determinatorism than anything, though, since he attacks Helio by himself, with none of his equipment, and immediately afterward you get to really beat the guy up.
Though your party faces Nene several times over the course of Blue Dragon, the only time you can actually engage him in a winnable battle is the very last time you meet him, with all your other confrontations falling into this category.
One of the most annoying examples is the Playstation 1 game Legend of Dragoon. In the arena scene you have to fight Lloyd, a major enemy of the game. He is undefeatable in the fact that he will simply dodge every attack you throw at him, and then, to add insult to non-injury, he mocks you with such phrases as "Ha! Not even close!" or "Don't waste your time!" or "Too Slow!"
One of the first few things you witness in .hack//G.U. is the cutscene version of a Hopeless Boss Fight, Haseo vs. Azure Kite Tri-Edge. Haseo is Perfect Play AIed so thoroughly and easily it is almost laughable. A variation of the same scene occurs at the end of the anime .hack//ROOTS since both series use that event as a buffer zone and it is no less brutal.
One of the .hack novels also features TheOne Sin, an event boss that many players of the game thought was Hopeless. It turned out to be a particularly intricate Puzzle Boss which doubles as an egregious case of That One Boss (probably to the point where if TV Tropes exists in the .hack verse and some of the players were Tropers, they'd probably think that it's an exception to the Bonus Boss rule for That One Boss!), and the two players who defeated it (Orca and Balmung) gained extreme notoriety.
Additionally, the 4th game features the final battle with Cubia. Once you win, it uses a move called Sephira Returner to restore itself to full health. Kite and Black Rose immediately conclude that the battle is hopeless. What they arguably lack in genre savvyness, they make up for in innovation, as obviously the game didn't end there. In case you were wondering Cubia is connected to Kite's bracelet, once Kite destroys it, Cubia vanishes with it.
besides the cutscenes, several boss fights in the Demon Palace Tournament cannot be beaten, such as the fight with Bordeaux and Alkaid. You could over level your character beyond the needed level for the moment and hit them one time reducing them halfway down their HP bar, and yet the cutscene will roll with it showing you getting your ass royally handed to you even if two seconds ago one blow from your opponent did no damage at all.
Digimon World 3 for the Playstation features Zambamon, a digimon that is WAY too powerful for your own digimon to defeat at the time you face him. In fact, he's so strong that the first hit he lays on your digimon, you are forced to flee. However, he is blocking the path to the next major city in the game, so you have to find a way to get him to move that doesn't require battling him anymore than the first time, which is required to advance the plot.
In the Amaterasu server, trying to force your way into Amaterasu City gets you into an unwinnable fight against Knightmon. To add insult to injury, it's virtually impossible to run away from the fight.
The Super Famicom game Dragon Ball Z: Legend of the Super Saiyan, Goku has to fight Ginyu. Like the DBZ story, Ginyu has to switch bodies with Goku in order to continue or you can just let Goku be defeated. The rest of the party has to defeat Ginyu.
Dragon Age: Origins has what appears to be a Hopeless Boss Fight after rescuing Anora from Arl Howe's estate in Denerim. You are confronted by Loghain's chosen knight, Ser Cauthrien, at the front door, and while after about 20 seconds of trying to fight her and her guards you think it's one of those times you have to just die, it's actually possible to win the battle if you're really good, and the story continues on as normal, except that Ser Cauthrien doesn't confront you before the Landsmeet, what with being dead and all. You get a sword for winning the battle, but you can also get this sword by killing Ser Cauthrien when she confronts you at the Landsmeet instead, which is much easier.
Winning this fight also lets you skip the 'Captured!' quest, where you either have to be rescued by your companions or break yourself (and possibly Alistair) out.
Though the final Mass Effect 2DLC, Arrival, doesn't feature any bosses per se, at one point, it pits Shepard (alone!) against five consecutive waves of frighteningly smart, increasingly powerful enemies in a room that has little suitable cover and no ammo refills except the ones you pick up from the enemies. You thought the Thresher Maw on Tuchanka was hard? Good luck getting the "Last Stand" Achievement. It soon proves that regardless of whether you are beaten to unconsciousness by the enemies or taken down in the cutscene following your "victory", you are taken prisoner and the villain's plan proceeds.
For the record, if you survive, the Reaper artifact "Object Rho" reaches full power and concusses Shepard into unconsciousness, whereupon s/he is sedated. (It doesn't stick.)
Two other DLC packs — "Stolen Memory" and "Lair of the Shadow Broker" — feature bosses that restore themselves to full strength whenever you get their shields down. In both cases, your squadmates will (eventually) rig up an environmental kill: Kasumi wall-crawls up to Hock's gunship and disables its shields while Liara brings down the ceiling of the Shadow Broker's lair, annihilating him with the biotic energy conduit contained there.
Mass Effect 3 has the first Kai Leng battle at the end of Priority: Thessia, which is similar to the Shadow Broker example above.
In Ar Tonelico 2: Melody of Metafalica, there is a boss fight with a guardian for the goddess, which also serves as the tutorial for Replakia. Despite using it at maximum power for as long as Cloche and Luca could possibly manage, one-shotting her guards and dealing millions of damage, she just won't lose that last hit point. In exchange, the boss will pull out a move that is nearly impossible to guard without seeing the attack at least once. Perfect Guards and your best healing magic can last for a while, but that attack will eventually hit hard enough to take everyone out.
This is actually used earlier in the game when you face three members of the Grand Bell one of them being Leglius, and all this happening after Cocona goes IPD. While you could possibly level grind high enough to beat these three, the fact is that you play as Croix and only Croix, have no backup or Revyteils meaning he cannot guard or be aided by song magic, cannot harmonize to use better skills, and will die quickly if not right away due to the level you should be at at this point.
The first encounter with Bradley in Dubloon. Considering he attacks you before you can even prepare your attack, he could just as easily beat you up in a cutscene*
Not even to mention his attack may do less damage than your hit point max.
In the Costume Quest DLC Grubbins on Ice, the game opens with you fighting three characters of a significantly higher level than you without a healer in your party. However, given some skill in hitting the button prompts and luck and the enemy's choice in targets, you can win. That said, the game assumes you lost anyway.
In Vampire: The Masquerade - Bloodlines the default solution to the werewolf level is to simply outrun the thing until the timer runs down. But technically you can defeat it by getting it to crush itself in the observatory doors, but this approach is difficult to pull off even if you've been consulting walkthroughs.
Demon's Souls partially-averts this with a seeminglyunbeatabletutorial level boss. If you actually manage to beat him, you are teleported to an area where you meet a boss from much later in the game, the Dragon God. He kills you in a cutscene, just to be certain you die this time.
In Dark Souls, Demon's Souls Spiritual Successor, the first encounter with Seath the Scaleless is one of these. You die over time while you can't inflict any damage upon him. When respawning, you discover that you are in a prison cell, rather than the last check point.
In Hyperdimension Neptunia, the first boss fight with White Heart, Black Heart, and Green Heart cannot be beaten for two reasons. Not only are you fighting 3 very high level opponents who blast you each once with their best specials, but Purple Heart is controlled by the AI in this fight, guaranteeing you lose.
In Winged Warrior III, the player is not supposed to be able to defeat the Nova Knight during the first encounter. It's possible to beat him after a lot of grinding at the training center, in which case the game will act up.
The Newgrounds flash game Mobile Weapon contains an example of this. At some point in the game, you fight Fleet Commander Ariel Highwater in her mecha, Serra Superion. The mecha has ridiculous health and power and will maim your party within a few hits. However, you don't lose the game: you merely need to repair your own mechas after the battle. You'll never hear from her again.
That's actually debatable. It's possible to grind a lot of monsters to level up to maximum level and stack up on repair items before facing her. She will still be, by far, the hardest boss in the game. Defeating her will not alter the plot at all, as she will just run away from you. You will, however, get a great sense of accomplishment from beating a very hard boss. Oh, and the infinity plus one grenade launcher too.
Rare Shoot 'em Up example in Chronos Twin DX. In the very first mission of the game, while you can be 'hurt' by regular enemies, nothing will kill you until you reach the boss, who exists across two timezones at once. He kills you dead by attacking from the past. The story then shifts forward several years to your character's younger brother trying again, this time with a modified time machine that lets him simultaneously be in the past and the present.
The flash game RPG Shooter: Starwish has the introduction level. You face against some easy cannon fodder Mooks... then you come across the Firebolt. This thing spams bullets and very damaging, hard-to-avoid lasers, and while you can beat it (doing so gets you a different cutscene and an achievement), it's very hard to do so and you'll probably go down.
And if you think you can curbstomp it in a New Game Plus with all your cool weapons, it also gets a health and damage buff and is just as difficult!
In the climactic mission, the plot called for you to lose your wingmen in battle with an enemy ace and make the final attack alone: however, this was achieved by having the ace magically respawning for so long as any wingmen not lost prior to that point were present. This lead to a surreal battle in which you might shoot him down a dozen times in a row, using up all of your missiles and countermeasures, and have no way of knowing what obscure action would cause things to proceed.
Similarly, forgetting to use a certain technology could also lead to a constant stream of respawning aces.
Finally, if you fail a critical mission and end up in the losing path, the final mission involves a confrontation with a unique Kilrathi capital ship which is almost impossible to kill without whittling it down with many minutes of firing. The expectation appeared to be for the player character to die trying so that the Bad Ending could roll. As you were not meant to destroy it, the game has no idea what to do when you beat it so just leaves you hanging in space.
While few in the Ace Combat series, "Shattered Skies" in AC04 may be the only one where there are enemy planes that are literally invincible: you'll never actually shoot down a Yellow Squadron member in that mission, although there's a dialogue line if you manage to hit one. There are two missions in Ace Combat 5 where you're actually unarmed (although you're actually very unlikely to get hit), and the series is sprinkled with missions where engaging the enemy aces would run counter to the mission objectives.
Of particular note is "8492" in Ace Combat 5, which pits you against multiple very tough enemy aces flying some of the best air superiority fighters in the game... right after a very taxing close air support mission, not allowing you to change your attacker plane for a more suited fighter jet between the two engagements. So although shooting down all of the enemy planes (as difficult as it may be) does result in mission success, unless you are flying a very advanced multirole jet, any sane person would rather simply flee, just as the story demands.
In Star Trek: Bridge Commander, there are a few times where you are encouraged to complete your objective and get the hell out of there ASAP, due to being highly out-gunned. A few times, ships respawn infinitely, but a few times you're highly rewarded for defeating all the enemy vessels.
In Descent: Freespace you can fight the Lucifer multiple times, but can only destroy it during the last mission due to its invulnerable shield. (This is because the final mission is the only time you encounter the Lucifer in the campgain where the "Invulnerable" flag for the Lucifer is not turned on. Yeah, that's right, the Lucy doesn't have shields, just a mission editor hax.)
Not that you'd stand much chance of destroying it even without the shields: you're a small, one-man fighter and the Lucifer is a 3 kilometer long superdestroyer. It takes a full squadron of fighters guarding two wings of heavy bombers armed with bombs meant for planetary bombardment to destroy it in the end.
Stealth Based Game
In Metal Gear Solid 2 Raiden goes up against 'Lady Luck' Fortune. Any shot fired at her misses, and any grenade thrown near her is a dud. Your only hope is to dodge her shots until events elsewhere force her to leave. The battle with the Metal Gear RA Ys counts as well, since Raiden eventually tires from the fight.
In Metal Gear Solid 3, when you encounter "The Sorrow" any sort of offense is useless since you can't hurt him or his spirits. The only way out is by convincing The Sorrow that you died, game over screen and all.
The DLC of Assassins Creed III has one against George Washington. Yes, THAT George Washington. If you run up to him, he blasts you away with an energy wave, if you run circles around him he'll shoot lightning at you, if you just keep your distance he'll summon thunder bolts from the sky on top of you.
Silent Hill 2 and Silent Hill 4 both feature unbeatable bosses. Silent Hill 2 has the ever-popular Pyramid Head, and after running away from him down a long, narrow, winding hall, blindly shooting at him, you run into an elevator to escape. Not everyone does though, and he manages to kill Maria. But only sort of. Eh. In Silent Hill 4, Walter Sullivan chases you for the entire second half of the game. He cannot be killed, but he can be slowed. He and PH do, however, eventually become beatable.
The two actual "fights" against Pyramid Head (in the apartment building and near the end of the game) definitely qualify. The only way to end these fights is to either die or wait until he decides to end it after a certain amount of time ( the first time by leaving the room, the second time by both Pyramid Heads impaling themselves on their own spears). However, while you can't actually "win" the fights, shooting him does shorten the amount of time it takes Pyramid Head to end the fight.
The final time Pyramid Head appears, there are actually two of him. Again, nothing James can do can hurt them, but if he survives long enough, they'll kill each other, simulateously impaling each other with their spears.
In the Gamecube Remake of the original Resident Evil, Lisa Trevor is an invincible deformed implacable girl super-zombie that stalks the player in several areas of the game. The final encounter with her is a Puzzle Boss fight where you have to push several blocks off a ledge to open her mother's coffin, causing her to jump to her death at the sight.
Although pushing the blocks off the ledge isn't the only way to kill her, as you can also forcibly push her over the ledge with your weapons.
Even then in the Wii rail shooter Umbrella Chronicles Lisa apparently survives her fall/suicide and becomes an unbeatable boss against Wesker during the Rebirth scenario. The least he could do against her was slow her down and pin her under a chandelier. It takes the mansion's self destruct system to finally kill her off.
Tragic Monster Steve in Resident Evil Code Veronica. Your only option is to run, and he will inevitably score a hit or two on you with his axe, which kills in two hits, so you better have some healing items on hand, or this may become an Unwinnable situation.
You can turn around and shoot him to slow him down (the explosive arrows are best for this). Technically, you can get away without a scratch. However, it is not possible to defeat him.
The T. Rex in the Dino Crisis series is an unbeatable boss, and if he catches up with Regina, he will swallow her whole. Although he cannot be killed, he can be slowed down with gunfire.
The first few encounters with the White Witch from The Dark Meadow will be this. You simply don't have the proper equipment or experience levels to deal with her, forcing you to investigate more of the game's story and kill more monsters first. And don't even think about winning against The Trickster's second and third forms on your first try.
The zombified Alan Morton, the final boss of Alone In The Dark The New Nightmare. No matter how many times you knock him down, he always gets back up. After stunning him, you have to run into a mundane alcove which contains a spear, which Carnby automatically uses to kill Morton.
Likewise, Obed Morton is so difficult to defeat that to many players he seems like a Hopeless Boss Fight, such that even most of the game's walkthroughs indicate the only way to finish the game is to use an exploit to run past him instead of fighting him. You actually can kill Obed by shooting him (and it doesn't even matter what weapon you use either), but you can only hurt him when he's in a certain pose (he should be knocked backwards if you hit him correctly, indicating you got it right).
In Fatal Frame 2, you have the Kusabi. An extremely powerful ghost, any time he appears before the end-game fight against him, he's immune to the effects of the Camera Obscura (rendering him invincible) and getting touched by him is instant death, whether you have a Stone Mirror or not. Your only option is to run.
The same game also features a sequence where the player must run from Sae Kurosawa, another extremely powerful one-hit kill ghost. In this case, though, she's invincible because the player has lost the Camera, and with it their only means of defending themselves against ghosts. Curiously, when she's encountered as the True Final Boss, she's no longer able to one-hit kill you.
The Fatal Frame series makes a tradition out of this: Kirie Himuro from the first game is also invincible and a one-hit kill until the final boss fight. The third game has Reika Kuze, who does not have one-hit kill powers, but is invincible until (you guessed it) the final boss fight.
Turn Based Strategy
Final Fantasy Tactics Advance has two of these, both of them involving Llednar. He's invincible and strong. You have to stall for several turns before the plot takes over. He does become beatable towards the game's end.
The challenge of the missions is lessened considerably if one equips the Damage to MP skill, since the one-on-one format means your character will always have MP to take the attack. It is likely the primary reason the skill was changed in the sequel to allow overflow damage to hit HP.
You could also steal his equipment to greatly reduce his attack power.
Just to give an idea of how unbeatable Llednar is: Most battles have objectives like "Win battle!", "Defeat the Boss!", or the suchlike. During the fight that's just Marche versus Llednar? "Survive!".
Disgaea 2 subverts this at one point. Initially, Laharl shows up and kicks your ass. However, in the process he breaks Rozalin's talisman, triggering her Superpowered Evil Side. This causes an inversion, where it is he who cannot possibly defeat you, however, you HAVE to lose, if you win this battle at the first phase then you get an ending and are forced to start the story from the top. The same with your battle with Etna. If you lose, the game continues, if you win, you get a joke cutscene, the credits roll, and you have to take it from the top.
Another Disgaea subversion happens during the first game. Initially, during the Chapter 6 fight against the Alternate Overlord, his group of ten is all at level 75, and you're normally barely breaking 30 on your first playthrough*
Meaning that should you lose, the castle retainers, their levels around 300 to 400, show up to bail you out as Neutral NPCs
. However, should you win this fight on another playthrough (or just level grind enough on your first time through), it turns out that the game just proceeds on. No special cutscene, nothing.
The Nippon Ichi game La Pucelle Tactics also had two such bosses, in chapters 4 and 8; defeating them earns a "special ending" for the chapter which grants a powerful piece of equipment.
Storywise, the only World Eater that falls under this category is Feinne, the first World Eater you encounter (right at the beginning of the story, to boot). Actually beating her triggers the battle against Asagi.
Rhapsody: A Musical Adventure loves to use this trope. Several boss fights (primarily with Marjoly's minions in early goings of the game) are impossible to win, simply because you can't damage them - all attacks will miss). Others later you have to at least survive for a few rounds before the game ends the fight. Still, the most amusing one is during the contest when you fight Etoile. You vs Rocket Launchers and Machine guns. Good luck!
Makai Kingdom actually inverts this at the beginning, placing you against a series of opponents whom you could not possibly lose to.
In Super Robot Wars: Original Generation 2, you are constantly pitted against the main bosses of the game — who retain their endboss-level stats the entire time. Whenever they show up, you're supposed to simply stay away from them until they leave, but one battle forces you to go all-out on one who is strictly unbeatable. In another, similar situation, the boss won't leave; either you leave, or you finally beat it by what amounts to cheating.
Should you actually win the first fight against the Inspectors (the Quirky Miniboss Trio), you get an awful lot of very good items, ridiculous amounts of gold and exp, and a rather amusing No Fourth Wall moment.
In Original Generation 1, there is the early and optional fight against Shu Shirakawa's horrendously broken Granzon. You are encouraged to run, although battling it is an option and a viable one at that, provided you have put a lot of money and level-grinding into Irmgult and the Grungust. Even then, the Granzon still takes a beating and only your top-tier units at the time should be used against it.
Warsong (Langrisser in Japan) had a non-boss version of this. In the first scenario you are supposed to escape, but a clever strategist can beat all the enemies instead. This has no effect on the plot except for a sentence or two.
In Fire Emblem, Captain Fargus challenges your group to see if they're worthy of being given passage to the Dread Island. If you select "Attack" instead of "Talk" when you do reach him, he will fight the character you used to challenge him. Since he's a pre-promote as well as extremely powerful yeah, you can guess the outcome.
Valter in the beginning of Sacred Stones is completely unbeatable, as was demonstrated on youtube to comediceffect.
The Invincible Black Knight in Path of Radiance shows up in an earlier mission when you are expected to not even have a promoted unit yet. Your goal of the mission is to escape the town by sea and if any, and I do mean ANY, character attempts to hold the Black Knight off...Well, they had a good run.
Radiant Dawn does something similar where the Not Quite Dead Black Knight is on the opposing side of the field in Part 3. Fortunately, he doesn't move until about 2 turns before the battle ends, which means he's no threat unless you deliberately step into his attack range. However, it does play with this Trope by offering you an interesting reward for challenging him; if Ike has a battle with him and SURVIVES (which requires a very high level at that part of the game), Chancellor Sephiran is playable for the Final Boss.
To make things more interesting, if you equip a strong enough unit with the Hammer-a weapon strong against armored units-it's actually possible to KILL the Knight(He's coded with the hammer weakness, even though he's only supposed to be vulnerable to certain blessed swords and magic). Doing this disqualifies you for the reward though, and he's not really dead anyways.
Battle Moon Wars, Stage 27: when it gets down to Weak!Shirou versus Archer, the game expects Shirou to hit 0 Hit Points and for the Shikis to have their Big Damn Heroes moment. However, it's possible without cheating to beat Archer; well, it would be, except when he hits 30% of his health, the script goes on as if Shirou had been defeated. You barely get a line of acknowledgment for your troubles.
Devil Survivor, Day 3: Beldr, first encounter. When NPCs say that Beldr is immortal, they mean it; his HP and MP are "???", and he nullifies everything. Your only option is to escort Midori out of battle, then have your party escape.
Devil Survivor 2, Day 7: Benetnasch, first encounter. It possesses a passive skill called Pacify Human, which naturally cancels out any attack from a human character... and then it pulls out the ability to forcibly unsummon your demons, leaving you no way to harm it and thus no choice but to run away until you can figure out a way to counter it.
You also can't harm Dubhe at first - the objective is to reach the other end of the map and escape, and losing any party member in the process results in an ordinary game over. However, just as you reach the escape area, it becomes blocked off and a cutscene results in Dubhe becoming vulnerable.
Sengoku Rance: If you fail to stop Miki from becoming the Demon King, you will enter the Demon King pseudo-route, and a Hanny will appear to your castle and tell Rance that there's absolutely no way to win. The enemy army will become incredibly tough by enabling all 4 buffs for every unit, greatly increasing troops sizes and fielding Kentarou and Xavier units with 8000 troops each against you. It's still possible to actually conquer all the enemy territories by using battle permits, but it will lead to Kentarou accusing the player of cheating and a standard Game Over anyway.
The first Sakura Taisen game had this in the first battle with the Koumas, where you're expected to fight for about one turn, realize your attacks are doing almost nothing, and run. In the PS2 remake, they're actually beatable, but the cutscene still treats it as if you ran away even if you stay and beat them.
In the Descent to Darkness campaign in Battle for Wesnoth, the final mission is essentially a hopeless series of boss fights. Mal Keshar is attacked by a hero and his/her army - it isn't hard to defeat them, but the mission will just repeat itself with new heroes until Mal Keshar is slain.
Ge Ne Sis: Reciful. The guy has 80,000 HP and reflects half of the damage dealt to him back to the attacker. However, you do get to fight him again straight afterwards using Esis, who is more than capable of dealing 80,000 damage in a single move, which is extremely satisfying.
Turn Based Tactics
At the end of Transformers G1 Awakening, the player is made to think that Shockwave must be defeated by Optimus Prime and Bumblebee. However, both Autobots are significantly weaker, even working together, and there are no power plants on this level that would allow them to level up. However, after Prime goes down, The Cavalry shows up in the form of Grimlock, who proceeds to Curb-Stomp Battle Shockwave.
In Bahamut Lagoon you have to fight against Sauzer/Zauzer in Chapter 5, but don't waste any items or energy, this guy has infinite HP, so you can't kill him.
Wide Open Sandbox
Shenmue has a character named Chai who is supposed to beat you; when you lose you're unconscious for several days, but the game isn't over. Beating him is nearly impossible, but can be done.
Shenmue 2 has one hopeless boss fight where Ryo fights Dou Niu and his henchmen in a plaza until the screen blacks out and shows a cutscene of Dou Niu beating Ryo.
Grand Theft Auto2 featured a mission that required you to "die" while attempting to break into an enemy gang's stronghold. Your employer then picks you up at the hospital and sends you back to the fort with a better plan and better equipment.
The original Grand Theft Auto featured a mission where you're asked to board a train as part of a plot to prove that your boss is the one true god. It's then revealed that the train is rigged with explosives. If you stay on it, after you die your boss apologises, saying that he was high on smack and is impressed you made it... Assuming that wasn't your last life. Worth getting off the train and failing just for the quote: "Only the righteous shall be saved! You! You are a shithead and bound for hell!"
In In Famous 2, the very first battle in the game is against The Beast, a being of overwhelming power that Cole is trying to become more powerful to defeat. In a surprising inversion, the battle is far from hopeless, as Cole ends up winning. Then the Beast breaks Cole, literally, and robs him of most of his advanced powers before breaking apart. It then reforms in Empire City, destroying it after Cole is taken south by boat, and the real game begins.
In Red Dead Redemption has the final "boss" of the mission where you kill waves of army and BOI agents just to end up making a last stand and getting shot by the main bad guy with a bunch of lackeys.
Non-video game examples:
Anime and Manga
This trope is parodied in the Suzumiya Haruhi side story "Haruhi Theatre Act 1". Haruhi and Brigade are trapped in an RPG, and when Haruhi meets a sage who warns her that she can't defeat the dragon without the power to do so, she doesn't listen and drags the Brigade over to fight it. Naturally she gets creamed and regenerates next to the sage, who smugly tells her off. She doesn't listen again and continually goes back and dies. When she finally listens to him, he demands some stuff from her as he's only giving them out if she gets quest items...but she just threatens him.
Captain Tsubasa, Japan Youth VS Hamburg SV (featuring Karl Heinz Schneider and half of his Germany team plus Wakabayashi), Japan gets beat down badly, and Hyuga can only score one goal because Wakabayashi lets him.
Fingolfin challenging Morgoth to single combat in The Silmarillion. He does actually manage to hurt him seven times but had no hope of actually winning.
Parodied in College Saga. The characters face Leviathan, who uses the devastating "Tidal Wave" attack, and quickly kills off the party... and then says "Just kidding LOL. You can't kill a guardian force."
The whole point of the Kobayashi Maru test in Star Trek. Like the Giant's Drink above, it's actually a psychological test rather than a tactical puzzle, although that doesn't stop people from trying. As various cadets' attempts to hack the infamous sim have piled up, they've resorted to ever-more-obvious tactics to keep it hopeless, including spawning extra enemies when needed or allowing them to break the laws of physics.
Virtually all tabletop RPGs run into this case (whether the DM wants to or not) if the players don't recognize a character as a major villain (or don't give a damn) and attack. Since many games take place in settings where Asskicking Equals Authority, the team of level 3 adventurers deciding to settle things with the ancient dragon lord tends end exactly as it should: in two turns (at most) with a room full of dead PCs. Entire sections of various dungeon-mastering guides have been dedicated to helping get powerful fiends away from a group of comparatively piddly heroes without having to murder them all.
In a rare tabletop game semi-example, there is Caine from Vampire The Masquerade. In one rulebook, there is a section regarding fighting Caine that consists of two words, "You Lose." To expand - he is the Biblical Cain, turned into the first vampire by God. He knows the disciplines of all vampires, centuries upon centuries of experience, and the ability to do - more or less - anything he wants.
In addition, he possesses the Mark of Caine from the Bible. Any damage inflicted on him is returned seven fold to his attacker. On the off chance someone did manage to kill Caine, they would instantly die.
Similar to the above example is Togashi Yokuni in Legend of the Five Rings. The utterly mysterious lord of the Dragon Clan, who is so enigmatic that those who speak with him don't even really remember what his voice sounded like or what words were said, is actually Togashi-Kami, the immortal child of the Sun and Moon and the only remaining sibling of the first Emperor. He is also a dragon. He can see the future and knows when he will die, and it sure ain't gonna be you that kills him.
Also similar to the above examples is the Lady of Pain in Dungeons & Dragons. She is the enigmatic steward and protector of Sigil, the City of Doors, whose motives cannot be divined and who can (and has) annihilate even higher tier deities with her power. She will flay you outright or trap you into a nigh-inescapable labyrinthine dimension should you ever do anything to cross her. Stats for her simply aren't given, because She > You no matter how many epic levels you've got.
In one of the Warrior Cats tabletop games included with a few of the books, if you attempt to fight a Twoleg, it becomes this trope. The PCs' only options are to attack, which does nothing but damage them, or run away.
In Sla Industries, two unstoppable badasses are repeatedly made mention of: the infamous serial killer, Halloween Jack, and the king and father of all Manchines, Digger. While both are a notable threats or inconveniences to the company, and have many attemps made against them, both are effectively unkillable: Jack has has a bounty of 2 billion credits on his head that no sensible op would try and collect on, and Digger has a whole army to fight with. Niether character has stats in any of the books, as they are considered to OHKthe party if they ever cross paths. This especially bad news for those taking one premade platinum mission, which requires them to go right into Digger's homebase, and sabotage his ultimate plan to conquer Mort.
Homestuck: There are a number of these, almost always going against the heroes:
Dave's first sword battle with his Bro was a doomed endeavour from the start, with Bro flash-stepping fast enough to use a PUPPET to fight Dave, and win easily.
John's off-screen encounter with his Denizen, whom Terezi caused him to encounter far too early, is implied to be this.
Almost every fight that the heroes have with Jack Noir, especially once he gains the powers of a First Guardian. Bro and Davesprite are the first to be beaten down, and his later encounters with John (stabbed before he can even raise his hammer) and Rose (killed despite having just awakened as a dark mage), followed by him slaughtering a THOUSAND robo-Aradias effortlessly, also go like this.
A surprising aversion occurs when Vriska goes off to fight him in the doomed timeline. Everything before that point implied that she would lose just as badly as everyone to face Jack before her, but due to her god-tier power of incredible control over luck, she rolls 8 8s on her dice, gaining a huge power boost, before actually putting up a decent fight against Jack. Whilst the outcome of the battle is uncertain (and wouldn't matter anyway due to it being in a doomed timeline as everyone else is dead), it's implied that Vriska might just have won.
Fridge Logic - what would you expect? Vriska's a Munchkin. She's the kind of person who WOULD win a hopeless boss fight.
Erf World is this for Parson, where he gets sucked into a game similar to one he designed, and realizes that since he wouldn't let his players win without cheating somehow, he won't win his battle either. At least not without trickery. He uses every loophole and unorthodox tactic he can think of to eventually defeat the opposing force.
Parson: "That, um, game I was developing at home...it had rules. But it couldn't be won within the rules. I wanted a game where the players had to surprise the GM with lateral thinking. So I was essentially going to cheat them. Undermine everything they tried. Until they found a clever enough way to cheat me. To break my rules, and win."