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