To unlock all 12 races for Time Trial, play through Tournament Mode. Note: Don't unlock all 12 races on Pipsqueak Difficulty

Unlockable	How to unlock
Dizzy Race	Successfully Complete Intermediate Race In Tournament Mode.
Expert Race	Successfully Complete Up Race (Original Edition) Or Neon Race (Gold Version) In Tournament Mode.
Glass Race	Successfully Complete Wobbly Race In Tournament Mode (Only In Gold Edition!)
Impossible Race	Successfully Complete Master Race In Tournament Mode (Only In Gold Edition!)
Master Race	Successfully Complete Sky Race In Tournament Mode (Only In Gold Edition!)
Neon Race	Successfully Complete Up Race In Tournament Mode (Only In Gold Edition!)
Odd Race	Successfully Complete Expert Race In Tournament Mode.
Sky Race	Successfully Complete Wobbly Race (Original Edition) Or Glass Race (Gold Version) In Tournament Mode.
Toob Race	Successfully Complete Odd Race In Tournament Mode.
Tower Race	Successfully Complete Dizzy Race In Tournament Mode.
Up Race	Successfully Complete Tower Race In Tournament Mode.
Woobly Race	Successfully Complete Toob Race In Tournament Mode.