Successfully complete the indicated task in Planet Superstars mode to unlock the corresponding character:

Alex Kidd: Successfully complete Tournament Singles in the "Alex Kidd" stage.
Amy Rose: Successfully complete Mission 2 in the "Sonic The Hedgehog" stage.
Gilius Thunderhead: Successfully complete Mission 1 in the "Golden Axe" stage.
Gum: Successfully complete Mission 12 in the "Jet Set Radio" stage.
MeeMee: Successfully complete Mission 8 in the "Super Monkey Ball" stage.
Pudding: Successfully complete Mission 1 in the "Space Channel 5" stage.
Reala: Successfully complete Mission 2 in the "NiGHTS" stage.
Shadow the Hedgehog: Successfully complete Mission 14 in the "Sonic The Hedgehog" stage.