Kenpachi's Story Mode path in Bleach: Blade of Fate is built around two-on-one battles. Of course, he's the one who's outnumbered, since he's too much of a Badass to have a partner. The first match is Byakuya Kuchiki and Renji Abarai. Byakuya can hit you from anywhere on the screen, and Renji has a massive number of distance attacks. Kenpachi? He has nothing that hits at long range. The best you can do is rush in and pray you don't get flanked. The second fight is against Hitsugaya and Hinamori, two of the game's biggest projectile users. Again, you can only rush in and hope you're not flanked.
Hanataro's (yes, Hanataro) story mode in Bleach: Shattered Blade, especially the fifth fight against Ikkaku. Forcing you to control a Joke Character whose entire movelist can heal the opponent against a CPU controller character with a hell of a lot more speed and range on his weapon? Boo on you, Sega.
In Bleach: Dark Souls, any level that makes you fight against the Grand Fisher. The son of a bitch cheats! And the first time, you fight him with Kenpachi, who isn't that bad a character but is utterly outmatched by Grand Fisher. A runner-up is the level where you play Orihime (who was needlessly weakened for this game) against generic Hollows, who deal far more damage than they should. It's an Escort Mission where you protect Hanataro, but Orihime is so slow and weak that Hanataro will have to do most of the work!
Mission 56 in Heat The Soul 6. Tessai and Captain Kisuke vs. Aizen. Aizen's HP and spirit bar are hidden, Tessai is a brand new character who you have no experience with, and Aizen has a lot of strong moves. And you lose if even one of your characters go down.
A few of the Championships in HTS6 are really annoying, as well. There's Mayuri's knockout battle which pits Mayuri and Nemu against, in order, Dordonii, Cirucci/Gantenbain, Uryu/Renji, Szayel and Orihime. You die once, you restart from Dordonii. And Orihime regenerates her health and loves to hide behind the shields she throws up periodically.
Super Smash Bros.. Brawl has a brutal level at the end of the Subspace Emissary which combines small portions every single other level. The player also had to go through and beat every single character they had unlocked yet (all but Sonic, Jigglypuff, Toon Link, and Wolf) and all bosses they had fought yet (all but Tabuu), making for a total of 43 fights. This level took up roughly 2 hours of play time on Easy mode. Luckily, you're able to save in the middle of the level, and switching characters also removed all damage.
There are some that can be bad on Intense, such as Battlefield Fortress, but the Canyon and Entrance to Subspace take the cake. Both of them are short, which would be a good thing, but what happens when the levels are made to be so short? Just ask undercoverfilmer00v if you get the chance. Don't get the picture? Well, what is going on is that there are no doors to serve as checkpoints, so the stages each have to be cleared in one shot. Oh, but here's the best part: at the end of both stages are Giant Primids teamed with tough enemies. You can abuse the terrain on Canyon to get around this problem, but not so much at Entrance to Subspace.
The Ruins. Bad enough on Normal, ridiculous on Hard or above. Nearly every single Goddamned Bat makes an appearance somewhere, as do a good proportion of the Demonic Spiders in the game. You've got the auto scrolling section with the mites knocking you back into the scrolling screen of death as you try to break down barriers of bricks in the path, a relatively annoying puzzle section with switches, a four battle platform ride where the terrain and enemies go from bad to worse, and well... it's downright annoying. At least there's an easy end battle and decent music thought. Also, agreeing with Entrance to Subspace, which is basically a Demonic SpiderBoss Rush.
Intense is That One Level. The Great Maze is actually pretty easy compared to, levels like the Meta-Ridley level. WHYYYYYYYYYYYY. Why did it take me 3 times to get past the first stage in that level. Oh right, Autolances and Metal Primids
Mario Bros. is this, because it's very difficult to get a KO because of the level's tiered layout. Plus, the enemies that spawn have huge knockback, even at low levels.
In the original Super Smash Bros., the Fighting Polygon Team is That One Level. You're always outnumbered 3 to 1 with each of those 3 being hard to hit and having an easy time outprioritizing you. As if that wasn't bad enough, you have to go through THIRTY enemies. At least the Fighting Wireframe Team in Melee were big targets (making them easy to kill) and there were only 15 of them that you go through quickly as long as you could deal with the low gravity in their case.
The 20th Floor of the Tower of Lost Souls in Soul Calibur IV easily qualifies with enemies that are equipped with auto guard impact S, auto negate throw (one of them has S rank) and one of them healing after guard impacts. The only way to win is to spam unblockable moves (best way is with auto unblockable).
Floors 30-32. You get one character. You cannot heal between fights. You have ELEVEN opponents in total to defeat. The last opponent has 200% health. Good luck.
The second to last group of floors includes groups of AIs that seem better than the highest difficulty available in vs mode. They also switch back and forth in the middle of combos to produce super combos. When you finally beat these three levels of hell, the Final Boss of the Ascension almost seems like the developers wanted to see just how impossible they could make a fight.
Level 71 in Soul Calibur II Weapon Master. Taki. Fucking Taki. Unless you're willing to cheat with a guard-ignoring weapon, you will run out of time.
The first mission in Thuban where you have to land a certain amount of hits on either Voldo or Taki within the time limit. Only problem is, they are both really damn fast. It's possible to cheat it and just ring out your opponent, but you have to give up any gold you would have won.
Super Smash Bros. Melee has Icicle Mountain. The random, often high speed, scrolling in both directions is a killer, especially for people that jump badly; it's good for your opponents, but not for you. You can often barely get in a hit either.
Cruel Melee is rather infamous for being one of the hardest, if not the hardest, level in the game. The enemies are very powerful and can KO you in one shot, plus they all gang up on you. The fields Big Blue and Poke Floats are both fast paced and jump heavy; in the case of the former you have to stay on cars - if you touch the ground you'll get swooped away.
The Omega forms of Ultimecia's Castle and Pandemonium are a pain to play in, especially against the computer. The former, because of the lack of solid ground and the computer is obsessed with going up and down the rails in the middle, meaning there's battles where you'll be standing there waiting for them to stop playing around so you can just finish the fight; and when it goes into Time Compression, half the solid ground will turn deadly with the gears. The latter because compared to every other level (except Chaos's arena), it's very cramped with many corridors, meaning there's both little room to dodge, and the camera will screw you up; and this one's twist is that the Stage Bravery is only increased when the red-ground spikes hit a character. Of course, the computer's reflexes are not going to let it get nailed, which means practically the only way to get the Stage Bravery high is when it hits you.
The Phantom Train stage introduced in the sequel might also qualify, as it is even more cramped than Pandemonium, consisting of a single, rather long train car. It's difficult to move around and, while the camera has been improved, it's still rather prone to swinging to bad angles where you might not see your enemy about to hit you.
In the storyline, the Ultimecia boss battle with Firion in Dissidia 012. The Bonus Line tells you to set Firion to Level 8. Ultimecia is Level 20, so she gets a huge boost to her Bravery. Firion is a ground-based Mighty Glacier with short-ranged attacks, while Ultimecia is an aerial-based Squishy Wizard with long-range attacks. Furthermore she has accessories that give her a huge boost to her damage output when she's far away from Firion and stays in the air long enough. All in all, Firion will struggle to get in hits while Ultimecia flies around the stage bombarding him with Knight's Blade and Knight's Arrow.
Three-medaling some of the Challenge stages is exceptionally difficult in Batman: Arkham Asylum, but the Extreme version (i.e. more enemies to fight, more special enemies) of Shock and Awe takes the cake, biscuit and whatever else it can lay it's hands on. You fight in a room where the floor is electrified - it's not active, but after a time limit, it switches on and you automatically lose. You face knife-wielders from the first round, baton-wielders from the second, both in the third and both with lots of regular mooks in the last. The regular mooks can also run to a gun cabinet on another level of the room. And you have to rack up 30000 points.
The difficulty only really ramps up in the second stage of the challenge, as that's when the normal mooks run to the gun cabinet, ruining your combos and forcing you to jump up while being attacked. The solution? Jump up onto the right-side platform at the start of each stage, and Ultra-Batclaw pull the mooks as they come up. You'll disarm any baton-wielders and it doesn't count against your combo status, allowing you to pull off the 30k score easy. Just make sure you use Takedown on the knife guys whenever you get the chance.
In Story Mode, later in the game when you have to re-enter the building in which you started, things will be much hairier the second time you get to the room with gargoyles. For one, you can only stay on a gargoyle for around three seconds before it blows up - and all six Mooks will be carrying a firearm, which means that a) you must disable all of them while on foot; and b) if you get found out, they'll pile on you and most likely kill you in seconds. The area's increased difficulty stands out in that, at least in Normal difficulty, no other area features such a spike in difficulty.
The final level in Chronicles of the Sword in Soul Calibur III. Your units can't heal, and if they're KOed, they're taken out of the level entirely. Adding insult to injury, the boss can regain health by attacking you. For someone without a good handle on anti-AI moves (or who doesn't want to use them), that level is an absolute nightmare.
If someone doesn't want to use the Anti-AI moves, they don't deserve any sympathy. The game sure as hell won't give it to them.
Chronicle 10 is pretty bad, too. Recurring Boss Hyle is holed up in the center fortress, and while he was only moderately difficult the two previous times he's fought, here he approaches SNK Boss territory. Your characters' moves are all powered down but his stay the same strength, and he's very difficult to take out in one round. Once he's finally defeated, you then have to deal with the Hellgenoss, eight powerful enemies that descend on the fortress immediately after Hyle dies. Fortunately they don't all arrive at the same time but it can still be rather overwhelming. Then after that, you have to deal with Kierkess and then Chester, who are both formidable bosses.
The Arctic Level in Twisted Metal2. While having huge chunks of the glacier fall away during the battle was a VERY cool idea, playing this level in multiplayer can be a pain. The chunks fall off bit by bit, leaving you and your friends fighting on a tiny bit of glacier. There's no way to set the level to not break away the pieces to give you and your friends a larger multiplayer level to play on.
Stage 7 of the Final Tower from Jump Ultimate Stars. You have to KO more than your opponent, but you have an incompetent AI for a partner, two of your four opponents are Bankai Ichigo and Gintoki, two of the best characters in the game, your opponents have ridiculously powerful supports, and you only have 30 seconds to win. And if you get a tie, there's no tiebreaker; you lose automatically. And you have to clear this stage if you want to unlock the last portion of the game.
Mortal Kombat Armageddon features a few. Most notable is against Kahn's statue. Though to be fair, it is near the end of the game. Arctika can be one as well, particularly if you're looking for the gods' armor.
Anytime your moves are sealed off in BlazBlue: Continuum Shift's story mode. The two worst offenders are fighting Unlimited Hazama as Ragna, whose Drives have been sealed off, and fighting Ragna and Unlimited Tsubaki as Jin, who can use neither his Drives nor his C moves.
Similar to the above example, there's a segment in Naruto: Ultimate Ninja 2 where Kakashi is locked out of using Ultimate Jutsu. And he has to fight several SNK Bosses during this time. There's also the battle against Kabuto that requires you to not only win (his health regenerates and his AI is ridiculous, for the record) but land the final blow with your Lv 3 Ultimate.