After playing this game a decent amount of time, I've found that there are secret moves that can be performed much like the bosses. I'm still trying to figure them out, but I'm making a bit of progress.
Slash:
B + X: Jumps up and then performs a downward flaming jump kick.
A + X: Breathes a flame in front of Slash that has slightly longer range than a punch.
Hack:
B + Y: Uppercut that knocks enemy down and does decent damage.
B + A + R: Jumps slightly backwards and dives forward with flaming knuckles.
???: Homage to Big Al from Rival Turf. Shout animation with chance for energy projectile from mouth. Most successful input is up slide to forward back to up repeatedly.
Wendy:
Up, full circle, B + Y: Wendy jumps and stands somewhere on screen, then jumps off screen and receives ~ 1/6 damage. After holding up for a long time, you can eventually make your way back to the screen.
Lord J:
None found, but possible throw reversal.
Kazan:
None found, but possible shuriken throw.
If you find some that I haven't, or can give detailed information on how to perform a move exactly, info would be appreciated.