Galuf's one-on-one fight with Exdeath certainly qualifies; every other playable character is powerless under the villain's Agony Beam, but the old geezer powers through it and inverts the Hopeless Boss Fight trope. Exdeath can't beat you in the following confrontation because he can still fight at0 HP! That's pure badass there.
Who could possibly forget Gilgamesh, walking embodiment (and humorous subversion) of this trope. Everything from his first appearance to his Heroic Sacrifice to his theme song is awesome, but his last words are the crowner;
...And he's back to deliver more in later installments; appearing as a Summon in Final Fantasy VIII, rather disappointingly as new forms in 9 and 11, but back to his true form in 12. In 13-2 he appears as a DLC boss with even more weapons than before. His grand entrances in 8, 12, and 13-3 are Crowning Moment Of Awesome level in themselves.
Hiryu has two Heroic SacrificeCrowning Moments Of Awesome. Not only does he arrive and sacrifice himself to save Lenna from being possessed by Melusine, but even after that, he waits at the top of the Phoenix Tower and sacrifices himself to give you the Phoenix summon.
The duel between the Great Sage Ghido and Exdeath. For nearly his entire appearance, Ghido has been this Deadpan Snarker turtle with a grim attitude and little patience for the naive heroes. Then Exdeath arrives, and Ghido shows he hasn't spent all his years chewing lettuceeatingpizza.
Faris leaping over a chasm to rescue Lenna from Magissa. Then she plummets to her death—except no, now she's climbing back up to throw a rope to the guys and deliver a righteous beatdown.