Final Fantasy IV: The After Years (The Lunarian's Story)
The Lunarian's Story follows Fusoya and Golbez into a bad feeling, near the beginning of the game's timeline (though being one of the very last chapters you play).
This is the first time in the game where you actually not only have a chance to survive against Mysterious Girl, but you're expected to kick her ass. An ass kicking LONG overdue. :)
5 versions of this run have been completed.