EOE Eve Of ExtinctionAgla cannot be damaged unless you use a Legacy weapon of the corresponding color they change into.
In Mega Man Powered Up, the Normal and Hard versions of the Wily Machine use the Robot Masters' attacks against you, requiring you to fight back with the weapon of the Robot Master it is strong against. However, Time Slow is useless against the Wily Machine when it is in Super Arm mode (it could only be harmed by Time Man's projectiles, and they're only available if you actually play as Time Man), but fortunately the Wily Machine doesn't attack during this state.
Henry in No More Heroes is the pinnacle of real difficulty. You have to manage to learn how to Dark Step, emergency evade and slash the hell out of him. He manages to be completely fair, despite his various unblockable attacks and his dreaded yet awesome One-Hit Kill, not to mention the Boss Remix "We Are Finally Cowboys" blaring in the background. The game actually makes sure that you're (hopefully) at the top of your game by requiring you to attain all beam katanas before facing off against him.
Yami in Ōkami manages to work in a use for every single Celestial Brush technique in the game, even if it has to make up completely new functions in some cases (for example, the Crescent technique normally just turns day to night, but in this battle, it summons Susano/Nagi to slice the boss vertically. Fitting, since the sword he wields is powered by moonlight. Still rather out of nowhere.), and the one and only Brush Technique that the Sequential Boss battle didn't require, and is otherwise useless (Sunrise), is its ultimate weakness in its final form.
Every game in this series is often set up so that you get a new item from a dungeon, learn a new technique, or receive special powers that will undoubtably play a major role in taking out a dungeon boss or the final boss.
The Shadow of Nightmares, the final boss in The Legend of Zelda: Link's Awakening. It morphs into a grand total of five different enemies you've fought before (excluding the Giant Bot), and if you're familiar with them, you know exactly how to counter their moves. Then, you have to endure the true form of the Nightmare, and the real final battle is underway.
The Ganondorf fight in The Legend of Zelda: Twilight Princess qualifies. In the very first part of the battle, against Puppet Zelda, you need to practice your defensive skills, such as your various dodging techniques, the Shield Attack, etc. The next section is played as Wolf Link, you have to use the trick you learned for catching runaway rams to beat him, and it involves some horseback combat. Wrap it all up with some serious need for the special sword techniques. Or distract him with the fishing rod.
Also from Twiligth Princess, Zant not only has you use almost every weapon in your bag, but even clues you in by changing the environment to that of the dungeon where you first used it. And still manages to make the solutions creative.
Majora from Majora's Mask is this, with each phase of the battle requiring a strategy that, in one way or another, mirrors that of a previous boss. But that's assuming you don't actually use the Fierce Deity Mask, which makes the "final exam" completely unnecessary. Granted, the Fierce Deity mask is harder to get than just beating the final boss, so in this case it's more like getting exempt from the final because you aced the entire rest of the class.
The Legend of Zelda: Ocarina of Time requires that you remember the Phantom Ganon battle to combat Ganondorf (or how to use a bottle in unorthodox ways), and figure out the Light Arrows are designed to smite evil. Running down the Tower forces you to face Stalfos again, who only drop their guard when attacking, but also regenerate if their comrades aren't all slain quickly enough, and hopefully you remember how to stop a Redead without the Sun's Song. On to the final battle, where Ganon swats away your sword. So, unless you got the Biggoron Sword, you have to use basically everything else in your arsenal: Megaton Hammer, bombs, arrows, even Deku Nuts. Finally, you have to unleash the Master Sword's Informed Ability at last- use it to deliver the final blow.
The final fight in Oracle of Ages rehashes an old battle wherein you had to use Mystery Seeds and the Switch Hook. Move on to simple swordplay and seed shooting, not to mention a couple tricks to find out how to move those Dark Links around. Finally, it's time to use bombs, sword, and seed shooter. Also, Pegasus seeds help a lot. Damn beetle form.
The Legend of Zelda: Phantom Hourglass has a final battle that involves the grappling hook, the bow, a new form of the drawing gimmick, and even some boat combat. To finish it all off is a form of swordplay you've been developing by battles against Jolene. And it is awesome.
In The Legend of Zelda: The Minish Cap: The first fight with Vaati requires a jar of winds, you need a bow for his next stage, and his final form requires the Cane of Pacci. The ability to multiply is also required for form 2 and 3.
In Metal Gear Solid 3, the Boss, while not exactly a final exam boss, does test almost all your skills learned in the game. You have to remain hidden, use camouflage, there's still food to hunt, she hides, you have to use your gunplay and most notably all your CQC skills. And MGS4 takes it to the extreme. The last fight with Revolver Ocelot incorporates strategies from the three previous games, even going so far as to change the health bar to match.
Mr. Freeze in Batman: Arkham City is invulnerable to frontal attacks and has a deadly freeze ray, plus he hunts you relentlessly through the area you fight him in. To take him down, you need to use every single different attack and gadget Batman has, because Freeze keeps activating countermeasures to stop you from performing the same trick twice. Curiously, this boss fight takes place near the middle of the game, rather than the end.
The Final Boss for Yu-Gi-Oh! World Championship 2010: Reverse of Arcadia has to be dueled multiple times, one for each form of gameplay in the game: first a race, then a Turbo Duel, then 2-on-1 (plays like a tag duel for your side), then finally a regular duel.
In the Carmen Sandiego game "Great chase through Time", the final stage is more like classic Carmen Sandiego games where you have to go to different time periods and ask the people there where they saw her go next. Normally, they give clues you would not get unless you've been paying attention to the general principles of the setting.
The final boss of Altered Beast for PS2 has six forms, each of which requires one of your transformations to take down.
First Person Shooter
The final battle of Half-Life 2: Episode 2 requires the player to use numerous tactics introduced throughout the game.
Wolfenstein ends with the player matching his Medallion powers with Hans Grosse, with access to each power being eliminated with successive stages of the battle.
El Toro in Wrath of the Black Manta. He only has 4 life boxes, but he can only be hurt by specific ninja arts... in order. If you use the wrong technique, he immediately regenerates to FULL life. More annoyingly, this happens even if you use the right technique, but from the wrong side of the screen!
The final boss battles against Gruntilda in Banjo-Kazooie and Banjo-Tooie. In fact, this is taken to the literal extent in Tooie, as Gruntilda will go easier on you if you correctly answer the trivia questions she asks during the fight.
King K. Rool in Donkey Kong 64. It's a five-round boxing match, and each Kong has to make use of their unique abilities to incapacitate K. Rool.
GLaDOS in Portal, only with portal-using techniques instead of weapons or powers. Even more obvious if you've heard the developer's commentary, which constantly keeps mentioning how the game is supposed to teach you how to use the Aperture Science Handheld Portal Device.
Also in Portal 2, where the use of all three types of gels and redirection of bombs is necessary to beat Wheatley.
The final boss of Prince of Persia: The Two Thronesnot counting the unlosable scripted part after the fight has three forms. The first is fought as a straight fight, the second requires you to use the environment to set up a Speed Kill, and the final part is a tricky platforming challenge, while being shot at by the boss.
In La-Mulana, the Mother has five forms, and each form must be defeated with a different main weapon, of which you have five of. In the remake, it qualifies as this, but in a different way. Sure, now it doesn't matter which weapon you use against her in each form, but she makes it for his final form, which gains new attacks based on the signature attacks of each guardian as certain amounts of damage is dealed to her.
Defeating Reflux in Rayman 3 requires the use of every Sealed Ability in a Can in the game. There's even a part where you dogfight him with a plane used in the penultimate level.
Bowser in Super Mario Galaxy makes use of previous spin techniques and such for defeating him when you battle him in Bowser's Galaxy Reactor.
The Titan Dweevil of Pikmin 2 attacks using poison, water, electricity, and fire. That's funny, there's a type of Pikmin invulnerable for each element used! As for the Purple Pikmin, their strength just helps kill it in its defenseless form faster.
Pikmin 3 continues this tradition with the Plasm Wraith. On top of being able to use every hazard in the game against you, it's piercing attacks can only be blocked by Rock Pikmin, and it'll often fly up high out of reach of even Yellow Pikmin, forcing you to use Winged Pikmin to attack it. Even getting to the actual fight requires you to have a good enough grasp on commanding and managing Pikmin.
The Rhythm Heaven series have these in the form of Remixes, which are basically mashups of the past 4-5 levels you've played. Then each game has a true Final Exam Boss in the form of Remix 6 for Tengoku and Remix 10 for Heaven and Heaven Fever.
The final boss of BIT.TRIP Core is a compilation of a bunch of patterns from the entire game, with the beats looking like asteroids that each move at different speeds.
The True Destroyer in Romancing SaGa 3. However, completely optional if you kill the Abyss Devil Lords beforehand.
The final boss of Wild ARMs 3 has a grand total of ten forms, most of which require the use of one specific spell in your repertoire. Then again, the Clive/Finest Arts trick deals so much damage that it can bypass any other trick you might be having trouble with through sheer brute force. The "Reflect" Spell can also cause a Crowning Moment of Funny if used against the right boss.
A literal example is from Ultima IV. Rather than fighting an overt evil, the game is about mastering the world's code of moral virtues and behavior. At the bottom of the final dungeon, rather than a tough boss, the player is quizzed on the virtues.
The final boss in Bloodnet repeatedly transforms into various major characters encountered throughout the game, requiring the player to use specific weapons and armor to take advantage of each form's particular weaknesses (for example, deflecting a cyborg's laser shots by wearing a reflector shield, or instantly killing a vampire with a consecrated blade).
Silver, the penultimate boss in Silver requires you to use all the magic you've acquired to destroy an object that is holding his power. Yes, even Healing orb and Time orb which normally have no offensive power on its own can hurt that thing.
Shin Megami Tensei games tend to have at least one boss like this in each game, but the requirements for each one are not necessarily as specific as many other examples. For example, in Digital Devil Saga, the final boss of the game requires you to smash orbs floating around it to destroy the boss. These orbs are each resistant to different elements, and the boss acquires said resistances from any orbs that are still standing. You don't need EVERY spell in the game, but you do need a good variety. The most common version of this in the series is a Sequence Boss, where the boss has a set pattern of abilities, and you must plan for all of them. In true That One Boss fashion, some of these bosses require to you get hit at times to avoid enraging them, like Trumpeter in Shin Megami Tensei III: Nocturne.
Nyx Avatar in Persona 3 has you go through each arcana one at a time, while not necessary to know what works for each Arcana, it helps.
And beyond Nyx, there is the secret boss, Elizabeth, whom you have to fight with only your main character, and who, like you, can change Personas, thus switching her weaknesses and defenses. You better know the traits of each of her Personas, and you better learn the partner of her fight and be equipped with a good variety of Personas yourself if you expect to win.
Chrono Trigger: Lavos's first form has shades of this, in the form of a Boss Rush you can heal between stages of. Do you remember how Magus's Barrier Shift trick worked? Or which hand to kill first on Giga Gaia? Oh, you'd better not have forgotten what dinosaurs are weak to. However, none of the bosses have scaled at all, so it's pretty likely you'll just brute force most of 'em with the benefit of dozens of levels. There's a bit of Fridge Logic there, too, as Lavos evidently took its DNA from the strongest creatures on the planet... who were promptly thrashed by the heroes. Also, at least one boss shows up from the future. And is a robot.
Happens with Emperor Sun Hai in Jade Empire, although to a lesser extent than many of the examples- he becomes immune to each type of style you use against him, so you have to repeatedly switch between Martial, Weapon and Magic styles to take him down. Or you can just hit Jade Golem Transformation.
In Mario & Luigi: Bowser's Inside Story, the final boss makes use of all the brothers' (and Bowser's) defensive actions (as series tradition). A better example, however, is the game's ultimate Bonus Boss. Bowser X is the final battle of the Boss Rush and temporarily disables any special attack the brothers can use after being used once. Add in a time limit on the fight, and that means the player is required to be proficient with just about every special attack.
The Sorceress' Tower in Kingdom of Loathing is this. First you must use potions, then meat pasting, clovers,and instruments, fight a regular monster, use combat items, heal yourself, and equip familiars, before you face a boss that is designed to stop your strategies (she takes away your buffs and often keeps you from using skills and combat items).
The developers have stated they consider this a weakness of the quest and game, as changes to the game slowly expand the potential set of resources a player might have, and it becomes less clear to new players why post-quest additions aren't working in a challenge they appear to fit. Rather than expand the exam or add alternate solutions when adding to the game, they'd rather abandon this trope entirely as a bad idea.
In almost all of the Pokémon games for handheld Nintendo consoles, you have to go through a cave called Victory Road before getting to the Pokemon League. This cave usually makes use of all of the HM moves that you acquired throughout the game.
"The Emperor", the final boss from House of the Dead 2, is a variation; his second attack pattern is to throw at you metallic clones of the previous bosses. These can only be stopped by shooting at their specific weak point, which you saw at the end of the original levels.
Taken even more literally by Typing of the Dead, where all the bosses test one particular area of typing note Judgment: reflexes; Hierophant: not looking at the keyboard; Tower: decision making; Strength: sentences; Magician: accuracy, and The Emperor is a test of pretty much everything.
In Typing of the Dead: Overkill, the final boss allows you to type any word you want in order to deal damage - as long as said word is somehow related to a displayed topic. The instructions before the fight even literally say Final Exam!