For me:
Boss: 343 Guilty Spark. I've wanted to kill that little robotic bastard since the original Halo.

Game: I'm going to say Metroid Prime 3 on the hard mode, except I haven't beaten it (IT'S HARD!)

Part of game: Any point in No More Heroes where you go DBZ crack mode and instantly kill everyone.

What about you guys?

Ok then lets do this again
Boss: Vergil (3rd time) DMC3 at the third time it gets to the point where you just want to stab him in the face

Game: Ninja Gaiden: Black. You try beating that on the hardest difficulty.

Part of game: Shooting somebody in the face with a torque bow on gears of war.

The part at the end of the third Prince of Persia (Not the weird acid trip.) Oh, and the part in Bioshock where you *fight* Andrew Ryan.
Chainsawing someone in half in GOW.

Boss: Beating that Gatekeeper in the ES: Oblivion expansion without attacking. Reflect damage enchants and healing spells for the win.
Part: Ditto.
Game: I'd have to say finally pipping lvl70 in World of Warcraft.

Boss: Covenant scarabs from Halo 3. Being able to take it down so many different ways, with at least a dozen UNSC marines(not including the hornets) all firing at it with rockets and machine gun fire while the monster blasts away at everything around it, makes for an awesome battle/boss experience.
Part: Anywhere in Halos 1, 2, or 3 where you get a bunch of marines fighting alongside you. This is especially fun in Outskirts and that little park area in Metropolis, where they can actually hold their own and do serious damage to the Covies stationed there. In Halo 3, this works for the first mission and the Storm. Vehicular madness...
Game: Metroid Prime. An excellent game, and a perfect transition from the 2-D platforming, to the 3D adventuring.

Boss: I just played the original Golden Axe and the final boss just made me wanna break my DS in half (I played some Sega Collection games that I found for the GBA and surprisingly Golden Axe was in it). Seriously, I spend nearly 10 minutes just trying to get a clear shot at him but those skeletons kept getting in my way.

Game: Ninja Gaiden on the original Xbox. I can barely stay alive in this game for more than 10 minutes.

Boss: Sander Cohen of Bioshock,If killing him wasn't enough the 360 version has an achievement for taking a picture of his corpse.

Part:The last request for beautiful katamari, Rolling up all of the continents and eventually stars and planets until you make a ball of crap so huge it clogs a black hole was great.

Game:Kingdom hearts, I don't generally play games for challenge(Online modes are an exception) so getting through the final bosses and finishing the game was pretty satisfying.

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