Artwork:
Win a track with a gold medal. Then, enter your profile menu and select "Progress". Highlight the track that was completed with a gold medal and press X.
Submitted by: Hunter

Classic mode:
Win a gold medal in each track in single race and tournament mode in four classes to unlock four classic tracks. Win a gold medal for all tracks in all five classes to unlock the classic tournament in all classes.
Submitted by: Hunter

Beta Tournament:
Finish in first place on all Alpha Tournament tracks.
Submitted by: Hunter

Ascension Tournament:
Finish in first place on all Beta Tournament tracks.
Submitted by: Hunter

Zone Team:
Finish with a gold medal on all Zone tracks (Pro Tozo, Mallavol, Coridon 12, and Syncopia).

Barrel-Roll Boost:
While in the air after any jump tap Left, Right, Left, Right to do a barrel-roll. Not only will you look cool but you will also get a speed boost upon landing!

Speed Boost:
If you press the accelerator the exact moment the light turns green to "GO" you start off with a nitro speed boost.

Livery Ships:
To unlock Livery mode, you have to beat Ascension Tournament with the Flash Class. If you use Livery mode, the ships will look a wee bit different.