Perform the following actions to unlock additional costumes for characters.

Peach Tennis Gear - Beat the extra levels Mushroom Cup
Black Mage / Red - Play 20 games with Black Mage / OR defeat in Flower Cup hidden routes / OR complete Star Road 6 times
Daisy / Tennis Gear - Play 40 games with Daisy or beat her in Flower Cup hidden routes
Ninja / White - Play 20 games with Ninja / OR defeat in Flower Cup hidden routes / OR complete Star Road 4 times
Slime / She-Slime / Metal Slime - Play 20 / 40 games with Slime or defeat in Star Cup hidden routes
Toad Blue / Yellow / Green - Play 15 / 20 / 25 games with Toad or defeat in Mushroom Cup hidden routes
White Mage / Alternate Outfit - Play 20 games with White Mage / OR beat her in Flower Cup hidden routes / OR complete Star Road 5 times
Yoshi Blue / Yellow / Pink - Play 15 / 20 / 25 games with Yoshi or defeat in Flower Cup hidden route