Here is the full list of all 16 Super Toy Cars 2 trophies - there are 13 bronze and 3 silver.
Win 1 Event
Win 1 Demolition Derby event
Win 100 events of any type
Play a multiplayer game either online or local
Use 10 power-ups
Use 100 power-ups
Use 1000 power-ups
Race 500 miles
Destroy 100 cars
Cross the finish line while being destroyed
Unlock all cups in Career Mode
Earn half the total points on Career Mode
Earn all points in Career Mode
Buy at least 1 car for each Vehicle Class
Buy all the upgrades for one of your cars
Acquire all cars in Career Mode