Mint (ToF) vs Bahamut (FFs) - Close. First, I think Bahamut wants his FF10 form for this match. This revolves around whether Bahamut can 2HKO. If he can, then there's no point in healing, and his initial attack forces Mint to blow her invincibility right away. I don't see Mint taking down Bahamut in that time. If Bahamut can't 2HKO, then Mint can respond to getting wounded by healing, then working her MP back up with attacks. It's possible she can't restore MP fast enough to have a good heal or invincibilty afterward, but in general, she can probably stall until Bahamut's overdrive gauge starts looking full, then go invincible and finish it.
So... according to the stat topic, Bahamut's physical does 9400 damage. Average PC damage is 7700, and Mint has mildly less HP than Rue IIRC, which means that Bahamut would baaaaaarely get the 2HKO... but I'm not sure I'd entirely stack Bahamut next to a single PC's damage, since he's taking the place of the entire party. Seems like some penalty should be in line for that (if not a 1/3 reduction). So I'm going to say that Bahamut doesn't 2HKO, and Mint lightly wins. It's still a darn close thing, though, as if Mint doesn't recover MP fast enough with her attacks, she won't be able to heal at all, and her later heals won't be full.