I have a few.
Sorceress Ultimecia and her GF in FF8. If all your characters are level 100, they get insanely strong and the GF (forgot its name) has some super death move that bugs me. And my Pheonix never helps when he does that move.
Metroid Prime from Metroid Prime. I don't know how everyone else does, but I can't kill the thing. Those darn Hunter Metroid keep on zapping me while I blast Prime with my Phazon gun. Only one more shot, but I died. Also, his annoying running across the arena and those energy shots that do so much damage.
Emerald Weapon from FF7. Ruby is harder (but was already mentioned) but this guy is annoying. His little orbs keep on blasting you, and I can't seem to get Knights of the Round ready fast enough.
Dullahan from Golden Sun: TLA. What really annoyed me was the fact that, after I tried the fight about 5 times, my friend, who had never played the game before, beat him in one shot.
Guildenstern from Vagrant Story. His ultimate move, Bloody Sin, is the hardest to block since its hard to predict when you have to block. Also, any weapon seems to do like 7 dmg to him, your attacks always miss after about 3 hits, he also moves really fast, and he'll stop all the way across the arena.
Fission Metroids. The fact that I can't freeze them, nuff' said.
Thats all I have for now.