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