Beat the game to unlock Free Run mode, Free Run Twin mode and Credits.
Face off Mode:
Beat Championship mode once to open "Face Off" mode against the Roadster.
Beat the Roadster in Faceoff mode to unlock it.
Beat the Tow Truck in Faceoff #2 to unlock it.
Beat the Saloon GT in Faceoff #3 to unlock it.
Beat the bus in Faceoff #4 to unlock it.
Thanks to Revolution readers Ryan Max and Dierdre Holly!