Here is the full list of all 39 Meow Motors trophies - there are 26 bronze, 8 silver, 4 gold and 1 platinum.
Obtain all trophies.
Win a Circuit Race on a damaged car.
Earn 15000 points for one drift race (career mode only).
Get 10x multiplier at Drift race (career mode only).
Win a race by playing for each character (career mode only).
Win a race by driving each car (career mode only).
Win all Circuit Races on 3 stars.
Earn all stars of all events.
Defeat the main villain.
Win all Drift races on 3 stars.
Complete all races of Revenge of Fire event.
Win all Strike races on 3 stars.
Hypnotize 20 opponents (career mode only).
Hit 3 opponents by Shampoo during one race (career mode only).
Hit 10 opponents by Gum Gum (career mode only).
Fix your car when the only one healt point remains.
Complete all races of Pumpkin Tour event.
Hit 15 opponents by Destroyer (career mode only).
Hit 50 opponents by Nuts (career mode only).
Complete all races of Waterfall Hills event.
Freeze twenty opponents by using Freeze Ray (career mode only).
Complete all races of Golden Season event.
Use Booster right on a ramp (career mode only).
Earn 25 stars of Drift races.
Destroy 15 cars of your opponents in Strike Mode (career mode only).
Ears 25 stars for Strike races.
Complete all races of Sea Battle event.
Earn 30 stars for Circuit races.
Complete all races of Frozen Way event.
Defend of Shark by using Shield (career mode only).
Complete all races of The Tree House event.
Complete all races of Skull Island event.
Hit 3 opponents by Shark during one race (career mode only).
Win a Drift race and don't touch the mines (career mode only).
Keep the best RPM.
Complete all races of West Fest event.
Shock three opponents by one Impulse (career mode only).
Eliminate an opponent by hit his car (career mode only).
Complete the training mission.