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