Here is the full list of all 33 Catlateral Damage trophies - there are 17 bronze, 10 silver, 5 gold and 1 platinum.
Complete 10 levels total in Objective Mode
Complete an objective without using paws
Meow a whole bunch
Get a score of 2,000 or more in Objective Mode
Max out all skills
Meow a lot
Don't knock over anything in a level
Only knock over 1 object in a level
Take a nap
Carry an object for 1 minute
Knock over 5,000 objects
Collect 10 photos
Play in Litterbox Mode for an hour
Get a score of 2,000 or more in Litterbox Mode
Be a cat for 30 minutes straight
Topple 150 unique objects
Knock over 1,000 objects
Topple 50 unique objects
Defeat the laser pointer
Stay airborne for 3 seconds
Catch a mouse
Complete the tutorial
Unlock all other trophies
Knock over 20,000 objects
Complete 50 levels total in Objective Mode
Unlock and complete the mewseum in Objective Mode
Unlock and complete the supermarkat in Objective Mode
Play with 100 cat toys
Catch 10 mice
Unlock all playable cats
Collect 100 photos
Collect 200 photos
Finish an objective in under 1 minute 30 seconds