Bear costume:
In Championship mode win all the Gold Medals in the mens events then press L or R at the character selection screen to access the costume.
Penguin costume:
In Championship mode win all the Gold Medals in the womans events then press L or R at the character screen to access the costume.
Robot costume:
In Trial mode win all the Gold Medals in the mens and womens events then press L or R at the character screen to access the costume.
Note: Using these costumes will disqualify you from winning Medals or setting Records.