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 race by playing for each character (career mode only).
Win a race by driving each car (career mode only).
Hit 3 opponents by Shampoo during one race (career mode only).
Destroy 15 cars of your opponents in Strike Mode (career mode only).
Hit 50 opponents by Nuts (career mode only).
Hypnotize 20 opponents (career mode only).
Win all Circuit Races on 3 stars.
Defeat the main villain.
Earn all stars of all events.
Complete all races of Revenge of Fire event.
Win all Drift races on 3 stars.
Win all Strike races on 3 stars.
Use Booster right on a ramp (career mode only).
Complete all races of Pumpkin Tour event.
Hit 10 opponents by Gum Gum (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.
Earn 15000 points for one drift race (career mode only).
Get 10x multiplier at Drift race (career mode only).
Earn 25 stars of Drift races.
Ears 25 stars for Strike races.
Hit 15 opponents by Destroyer (career mode only).
Complete all races of Sea Battle event.
Win a Circuit Race on a damaged car.
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.
Win a Drift race and don't touch the mines (career mode only).
Hit 3 opponents by Shark during one race (career mode only).
Shock three opponents by one Impulse (career mode only).
Eliminate an opponent by hit his car (career mode only).
Complete all races of West Fest event.
Fix your car when the only one healt point remains.
Complete the training mission.
Keep the best RPM.