Beat the following Grand Prix or Time Trials to unlock the race mode.

Grand Prix or Time Trial	How to unlock
Mirror Grand Prix	Win a Grand Prix or Time Trial.
Mirror Time Trial	Win a Grand Prix or Time Trial.
Racecourse Challenge	Win a race in Time Trial.
Rainbow Raceway	Win a 2 races in Grand Prix.
Reverse Grand Prix	Win a Mirror Grand Prix or Mirror Time Trial.
Reverse Mirror Grand Prix	Win a Reverse Grand Prix or Reverse Time Trial.
Reverse Mirror Time Trial	Win a Reverse Grand Prix or Reverse Time Trial.
Reverse Time Trial	Win a Mirror Grand Prix or Mirror Time Trial.