Here is the full list of all 12 Stunt Paradise trophies - there are 11 gold and 1 platinum.
Get every Trophy in the game
Complete the first level
Destroy the police car in the first level
Perform a double backflip and land on your wheels
Perform a double front flip and land on your wheels
Blow up your car
Sink your car in water
Use Nitro 3 times
Earn 5000 coins
Buy a new car
Get 5 stars
Complete 10 levels