Here's a list of Abilities from Josh & Jack's All Star Battlers. Some are only available in RPG, some in arcade & story mode.
Story & Arcade Mode
Characters
Josh the Hedgehog
Punch : Circle
Kick : Square
Sword Slash : Triangle
Charge : X
Shoot : (Circle - Left/Right Arrow) (depending on what direction you face the enemy)
Combos
Tachyon Combo : 2x Square > 3x Triangle
Tachyon Kick : Up Arrow > (1x Square - Right Arrow)
Zap Rifle Shooting : Down Arrow (Circle - Left/Right Arrow)
Ancient Gamma Blast : Up Arrow (Circle - Left/Right Arrow)
All Star Art: Tachyon System : (Down Arrow - Circle) L / R Button (depending on what direction you face the enemy)
Form Change (Ascend) : (X - Up Arrow)
Form Change (Elemental) : (X - L / R Button)
All Star Finisher : (X - Left or Right Arrow) (depending on what direction you face the enemy)