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