Either complete the race in first with the Golden Wheel or do Challenge Mode.

Unlockable	How to unlock
Doc Hudson	Complete Rustbucket Stadium Elimination.
Fillmore	Complete Underground Run Beat The Clock.
Flo	Coming in 1st in Ornament Airport with the Golden Wheel.
Lizzie	Come in 1st in Tailfin Pass with the Golden Wheel.
Luigi	Main Street Elimination.
Ramone	Complete Tailfin Pass Trophy Hunt.
Sarge	Coming in 1st in Willy's Butte with the Golden Wheel.
Sheriff	Coming in 1st in Main Street with the Golden Wheel.