Ouroborus- Bravely Default- Mainly for the creative use of spotpass.
Perfect Chaos- Sonic Adventure- Doesn't really hold up, but the combination of the visuals and music were pretty epic in 1999. Having a Sonic Boss where your objective is to run real fast was a smart choice.
Eggman- Sonic Colors- Purely for the theme song.
Xenmas- Kingdom Hearts 2- Kingdom Hearts did an amazing job of taking what was honestly a pretty basic battle system and making it feel cinematic and epic. Nowhere better than in the climax of Kingdom Hearts 2.
HHH- WWE Day of Reckoning- In wrestling and videogames, the key to a great climax is building a grudge between the protagonist and the antagonist. In the storyline of this really underrated game, HHH is the villain, manipulating your character from the beginning. When you eventually get the chance to beat him for the championship, it's pretty awesome.
Sandman- Punch Out!!!- A simple but challenging test of the skills you've learned over your boxing career.
Jeringha- Wonderful 101!- Platinum games is great at doing ridiculously over the top final boss battles. This one is my personal favorite.
Undertale- Whichever route you go with, the final boss is an appropriately epic culmination of your character's lust for power or unflinching kindness. Also features two of the best tracks in gaming.