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