Divinities
Depth Dragoon (Mega Man X Command Mission) vs. Jenna Angel (Digital Devil Saga): Boost speed twice, spam Thunderclap to cancel any Jenna turns probably. He can probably just tank Bhairava with buffs too. Jenna's own debuffs are pretty paltry by comparison.
Yuna (Final Fantasy X) vs. Loki (Valkyrie Profile): She has a pretty good argument to take this without aeons, idly. Phantom Ring deals with Extension Force and should greatly reduce the potency of Indiscrimate, especially with Shell as the first action. Obviously in practice whatever, summon+magic as often as needed takes care of things.
Demigods
Emily Bell (Suikoden 3) vs. Magus (Chrono Trigger): Yeah no, the physical walling is too strong, here.
Shania (Shadow Hearts 3) vs. Worker 8 (Final Fantasy Tactics): Buff self so that W8 hardly scratches her exact with moves which suicide, heal as needed, hit him on his own turns (wouldn't see him countering, both the fact that La Sirene uses thrown energy orbs and the fact that Hard Hit knocks the target across the battlefield make me confident she can get around melee counters if need be. Although I think she can take this even if you disagree).
Heroes
Maria Traydor (Star Ocean 3) vs. Rune Walsh (Phantasy Star 4): Block ID, use turn 1 paralysis. She's fortunate that she uses physical status of a type Psy equips don't cover, because status isn't turn 1 against Rune too often! So it goes.
Belcoot (Suikoden 5) vs. Guy (Fire Emblem): Hmm. Guy doubles, goes first, and certainly isn't killing in less than 6 hits (5's enough to me), so with a counter in there he should be able to kill on his second turn. So Belcoot needs a OHKO. That's... very unlikely, as Guy's high speed and luck will reduce his 2x-swing and crit rates even further, and he does need one... just misses a OHKO without it (98% damage or so). To make matters worse Guy might even evade, although that's not too likely with Belcoot's good accuracy.
Lawfer (Valkyrie Profile) vs. Odie (Soul Nomad): Odie doesn't have any defensive advantage against spears, so I think Lawfer should OHKO him?
Angelo (Dragon Quest VIII) vs. Basilio (Fire Emblem Awakening): Faster, isn't OHKOed, and has instant death which certainly isn't worse than turn 2 here (50%).