You have to do different tasks to unlock the characters.
Unlock Slime:
Win 28 games.
Unlock Cactuar:
Win 60 games.
Unlock Moogle:
Complete the Mushroom Cup tournament.
Unlock Black Mage:
Complete both Star Roads located on the Star Cup map.
Unlock Ninja:
Complete one of the two Star Roads located on the Star Cup map.
Unlock White Mage:
Complete both Star Roads located on the Star Cup map.