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