Here is the full list of all 51 The Sims 3 Pets trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Unlock all other trophies.
Complete each of the Sim happiness Challenges.
Escape a karmic backlash by quickly balancing the meter after dropping below -50.
Fetch a date.
Steal something worth at least §2,000 with a cat.
Activate the Cry Havoc karma power during a wedding party.
Complete each of the k9 cop scenario Challenges.
Find your lost pet.
Complete each of the dancing Challenges.
Scare the reaper.
Complete each of the Cat-astrophe scenario Challenges.
Promise and complete a pet-related Lifetime Wish.
Send a simbot back in time.
Complete each of the Leonardo Reborn Sub-Challenges.
Catch every ghost spawned by the Ghost Invasion karma power before it ends.
Train a pet to have 9 traits.
Find a special plant while fishing.
Complete each of the explorer Challenges.
Make a Sim transmogrified from a cat and a Sim transmogrified from a dog become a couple.
Complete each of the mystery chapters.
Explore the Abandoned Mine in search of Timmy.
Complete each of the love and romance Challenges.
Complete each of the parenting Challenges.
Use a telekinetic cat to make a Sim fix a meal from the fridge.
Complete each of the fishing Challenges.
Complete each of the exhibitionist Challenges.
Deal with the feline in the Dog Days of Summer mystery.
Discover the lost pirate ship anchor.
Avoid the zombie bears to find the pirate ship's log.
Complete each of the relic collection Challenges.
Create a flux combobulator.
Successfully bathe your cat.
Praise or scold a pet enough times to add a trait.
Punish the Sims for their crumb-filled, sub-standard furniture.
Target your neighbor with the Ghostify Power, then catch them with a cat or Ghost Zapper.
Complete any 10 Skill Journal Milestones.
Destroy §10,000 worth of objects with a dog or cat.
Have your Sim kiss their brother’s/sister’s best friend.
Get the attention of the Socialite Club.
Build a house with 5 stories and an unfurnished value of at least §100,000.
Build your house from the ground up by replacing your property with an empty lot.
Become a romantic interest of your boss.
Go to work with 4 career performance requirements at Outstanding.
Breed a Natural-Born Hunter cat or Natural-Born Digger dog.
Make out with the maid.
With a pet, steal a Sim's clothes who is skinny dipping.
Reach level 10 of a career.
Fetch something worth at least §2,000 with a dog.
Earn more than §1,000 during a trick exhibition.
Have a dog and a cat become best friends.
Become a BFF with a dog.