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As defined by the events that take place in the video game:
Sonic Unleashed Final Boss - The music was a heavy contributor, as the boss itself was actually rather easy. The actual progression of the boss, however, was quite helpful as well as the sheer sense of scale.
Super Metroid Final Boss - The gameplay was actually not nearly as difficult as Ridley. If you've played it, you know why, if not... you should play it.
Okami - There were actually two such occasions here, the first being when one of the bosses appeared to have the same ability to use the canvas that you did, and the second being the final boss which was quite strenuous and a mid-battle event that was somewhere between "heartwarming" and "epic".
Bugs Bunny Double Trouble - The game was very difficult, so I seldom made it to the Arabian level, but when I hopped in my spaceship and chased Marvin, it was close enough to an end-game event for me.
Ristar Final Boss - Theme of Kaiser, you slowly are levitated to his throne room as he commands his servants attack you, then everything goes crazy and he even opens a rift in the fortress to suck you out.
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As defined by personal accomplishment:
Cave Story - Running Hell, 'nuff said...
Super Metroid Ridley - It didn't help my nerves any that I thought I was going to die on that last hit...
Super Metroid Redesign Norfair Run - I had one health bit to spare from the first area, savestates and guidance from Prime could not detract from it.
Super Metroid Redesign - I still have yet to face the Phantoon, but every time I play it, I end up pulling something off I would have not believed I could have before.
Mystic Realm - When I beat the game legitimately, Prismatic Angel was the real accomplishment (played on three lives per try to boot), but Mystic Realm was the icing on top.
Sonic 2, Sonic 3, Sonic 3K Final Bosses - Now I could probably beat them with my eyes closed (umm, some peeking perhaps), but when I first played them, these seemed impossible. ESPECIALLY Sonic 2.
Brawl - Defeating Tabuu was no easy task. Even with my brother and I both working at it together we only won by chance.
Welcome to the Machine - The last levels in Ecco are really, really difficult. The vent was difficult but need only be played once, beating the machine was a true sense of accomplishment, eclipsed by the disappointment of having to repeat it after the queen killed me.
City of Forever - Ecco II had an even MORE scarring final encounter. While the boss was easy (most of them were except for the stupid globe holder!), you had to follow an invincible vortex larva that can OH-KO you through a Atlantean labyrinth. I spent 90% of the time hiding and trying to avoid them, but only the larva can open certain doors. Actually beating the level still was nothing compared to turning the corner to run into the arms of the larva and have the wild, furious burst of hissing sound as it crushed you in its embrace.
EDIT:
TrueTenguMan said:
*Unlocking the secret mission during the zerg levels in starcraft: brood war ( think you had to beat it under 3 minutes? I forgot, but the limit was around there..)
I wish I could reference a Starcraft accomplishment, but I can't remember which ones I did legitimately. I think I was actually forced to unlock that mission without cheating which makes me wonder how I ever got there.