Here is the full list of all 16 Pocket Race: Driver achievements.
Win your first race
Win two races
Win three races
Finish without explosion
Push 10 cars off the road
Win a 4 track season
Win a 12 track season
Win a 12x2 track season
Buy a new chassis
Buy the best chassis
Buy the best motor
Buy the best battery
Buy the best wheels
Draw a golden card
Destroy with Monstercar
Collect 66 batteries