Here is the full list of all 38 Riff Racer - there are Race Your Music achievements.
Drive ALL cars
Unlock ALL packs
Unlock 20 packs
Drive 50 songs
Drive 10 cars
Play a Classical song
Drive 5 cars
Race on a song longer than 10 minutes in length
Unlock 10 packs
Play a Jazz/Funk/Soul song
Reach Driver Level 20
Score more than 100,000 on a song under 3 minutes in length
Author 10 tracks
Drive 25 songs
Reach Driver Level 15
Beat a friend's ghost
Play a single song 10 times
Reach Driver Level 10
Author 5 tracks
Stay in the super-sync zone for 25 consecutive seconds
Reach Driver Level 5
Unlock 5 packs
Drift more than 16 beats in one manoeuvre
Drive a whole song without hitting a barricade
Drive 10 songs
Play a Pop Song
Beat a recommended ghost
Smash 30 boxes or more without missing one
Boost 20 times or more in one song
Enter the super-sync zone 10 times in under 40 seconds
Play a Rock/Metal song
Play a Hip-Hop/Urban song
Jump more than 8 beats in one manoeuvre
Roll more than 4 beats in one manoeuvre
Stay 100% in sync for a whole song
Author 1 track
Play a Dance song
Drive 100 songs