Successfully complete one of the following tasks to get a trophy:

12-Wheeler (Bronze): Create a model car with at least 6 pairs of wheels and beep the horn.
Best Friends (Gold): Stroke your pet at least 30s a day for 5 days in a row.
Day 1 Mastered (Silver): Complete all Day 1 challenges at gold level.
Day 10 Mastered (Silver): Complete all Day 10 challenges at gold level.
Day 11 Mastered (Silver): Complete all Day 11 challenges at gold level.
Day 12 Mastered (Silver): Complete all Day 12 challenges at gold level.
Day 13 Mastered (Silver): Complete all Day 13 challenges at gold level.
Day 14 Mastered (Silver): Complete all Day 14 challenges at gold level.
Day 15 Mastered (Silver): Complete all Day 15 challenges at gold level.
Day 2 Mastered (Silver): Complete all Day 2 challenges at gold level.
Day 3 Mastered (Silver): Complete all Day 3 challenges at gold level.
Day 4 Mastered (Silver): Complete all Day 4 challenges at gold level.
Day 5 Mastered (Silver): Complete all Day 5 challenges at gold level.
Day 6 Mastered (Silver): Complete all Day 6 challenges at gold level.
Day 7 Mastered (Silver): Complete all Day 7 challenges at gold level.
Day 8 Mastered (Silver): Complete all Day 8 challenges at gold level.
Day 9 Mastered (Silver): Complete all Day 9 challenges at gold level.
Excellent Owner (Silver): Pass 20 Pet Reports.
Fish Fascination (Silver): Fill your aquarium with every type of fish.
Flying Saucer (Bronze): Make a model plane that's only a wing and made of metal and fly it into space with your pet dressed appropriately.
Gold Rush (Gold): Complete every challenge at gold level.
Gourmet Pet Food (Bronze): Unlock every type of cookie.
Green Paws (Bronze): Fill your garden with different flowers.
One Good Day (Bronze): Pass a Pet Report.
Pet Artiste (Bronze): Teach your pet 50 drawings.
Pet Panic (Bronze): Wake with a fright then stroke your pet back to sleep in 40s.
Platinum Pet (Platinum): Unlock all other trophies.
Prize Bonanza (Gold): Unlock every prize.
Shopaholic (Bronze): Download 1 free item from the EyePet store.
Solid Silver (Silver): Complete every challenge at silver level or higher.
Songbird (Bronze): Teach your pet 25 different songs.
Speed Wash (Bronze): Wash your pet in under 60s.
Stunt Pilot (Bronze): Break 140 mph in a model plane without smashing into the ground.
Style Icon (Bronze): Give your pet 10 new looks.