Here is the full list of all 17 Super Toy Cars Offroad trophies - there are 6 bronze, 6 silver and 5 gold.
Win your first event!
Play a local multiplayer event
Win 100 events of any type
Drive 500 miles
Finish 1 cup in career mode
Finish half the cups in career mode
Finish all cups in career mode
Acquire all the vehicles in the career mode
Unlock all the paintjobs for all the vehicles in career mode
Acquire all the upgrades for a vehicle in the garage
Drift for an accumulated distance of 25 miles
Use 10 power-ups
Use 100 power-ups
Use 500 power-ups
Destroy 100 vehicles
Drive 100 miles in a single vehicle
Win 1 event of type Drifting Challenge