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