To unlock a bear costume, finish Mens Championship Mode with an overall rating of first place. You will then be able to select the suit while choosing a character.
To unlock the Penguin costume finish Women's Champoinship in first place.
To get the Robot costume, win a gold medal in Trial mode in all male and female events. Then press R-shoulder on the character select screen.
(Note- you cannot earn medals while wearing either of these costumes)