The costumes are unlocked by clearing all missions with A's with each character. Knuckles gets a PSO suit, so does Sonic & Shadow. The Cyclone turns red and the Eggwalker turns black and Eggman wears a semi-gangster hat. Rouge has a PSO-based costume, too. Hyper Shadow doesn't exist. Hyper Knuckles and Super Tails are only in S3&K. Turbo Tails is an Archie character. Super Sonic is also not a hidden character, but is only accessible during the Final Hazard along with Super Shadow.
~ SA Tails, Crazy C Lea, & True Red