To unlock Mini Games, start by earning medals in the first mini-game:
Ayame's Shuriken minigame: get at least 500 medals
Gunrock's Slot minigame: get at least 1000 medals
To unlock Powerstone 1 Unlockable Characters, do the following:
Accel: complete the game with Gourmond
Gourmond: complete the Game with Julia
Julia: complete the Game with Pete
Pete: complete the game once with any character
To unlock Powerstone 2 Unlockable Characters, do the following:
Mel: complete 1 vs 3 mode with Pride
Pride and Kraken: complete 1 vs 3 mode with Falcon
Valgas: complete 1 vs 3 mode with Kraken