I honestly can't remember if anyone has done this type of thread since it was released... Anyway...

My favorite story boss is probably going to be any fight with the Judges or the Espers. Specifically Judge Bergen and Judgemaster Gabranth, and for Espers, it's Belias and Famfrit.

For unimportant story bosses, probably Firemane, Elder Wyrm, and the battle with the Mandragoras

For Mark Hunts: Deathgaze, Pyrlaster, and Fafnir

For Elite Marks: Gilgamesh is a given, Carrot was fun, Orthros was amusing, and the Shadowseer fight was awesome.