All characters:
Pause game play, then hold L and press X, B, Left, Y, Right(2).

50 balls:
Pause game play, then hold L and press Up, X, B, Y, Left(2).

Never get hit by items:
Pause game play, then hold L and press X, B(2), Left(2), Y, B.

Have fruits during entire race:
Pause game play, then hold R and press B, X, Left(2), Y.

Flying abilities for any character:
Pause game play, then hold L and press X, Y, A, Left(2), Right(2).

Gex:
Successfully complete the game with all three default characters in time challenge, stunt challenge, an cash trial modes with all medals. Alternately, collect all the status decals in the game.

Hex:
Successfully complete the game with Chops, Sid, and Zero-G to unlock Hex as a selectable character.

Roscoe:
Collect 20 Hex Bux in all eight levels.

Synder:
Get the time challenge goal for every level to unlock Synder.

Tek-9 glider:
Successfully complete the game with any character to unlock the Tek-9 glider.

Tremmel King:
Win all three shortcut medals in all eight levels.