There are 40 Trophies that can be collected.

Bronze

Always Land on my Feet
Complete a best of three team challenge

Adios, Amigo
Boot an enemy into a trap

Ole!
Block an enemy attack

Touche!
Perform a deflect

Scratch That
Perform a Claw Frenzy

Pet Peeved
Defeat 3 enemies with one guitar attack

Virtuoso
Play every guitar tune

Swashbuckler
Bronze medal on every level

Silver

Holy Frijoles
Defeat 20 enemies using the guitar

Looking Sharp
Defeat 10 enemies using Claw Frenzy

Over Easy
Collect all nine golden egg pieces

Pray For Mercy
Collect all nine wanted posters

Light on my Feet
Perform a perfect sneak

Copycat
Perform a perfect shape-match

Well Balanced
Perform a perfect balance

Feisty Feline
Get a high score in Market Mayhem

Purrfecto
Get a high score in Barrel Barrage

Viva Gato!
Get a high score in Shape It Up!

Real Cats Wear Boots
Get a high score in Bandit Boot

Such Moves, Such Handsomeness
Get a perfect time in the Beanstalk

Don't Desert Me
Get a perfect time in the Canyon

Care to Dance-Fight?
Perform a perfect dance in the Cantina

Purrrrrrfect Score
Serenade three different senoritas with a perfect score

Hero
Silver medal on every level

Gold

These Eyes Tell No Lies
Discover every type of trap

Legendary
Gold medal on every level

Platinum

The Cat's Whiskers
All other trophies have been collected

13 Secret

Bronze

I Thirst for Leche
Complete The Thieves' Bar

Me-ow!
Serenade a senorita

En Garde
Defeat the cat lover

Check me Out
Complete The Hotel

Born with Cat-like Moves
Complete The Chase

Nice moves, Senor
Complete The Cantina

Stage Complete
Complete The Stagecoach Robbery

I Flirt with Danger
Rock a pig back to sleep. Only in Adventure Mode.

Wild Goose Chased
Complete The Giant's Castle

Conquistador of the clouds
Complete The Beanstalk

This Cat is En Fuego
Complete The Mine

Danger is my Game
Complete The Great Terror

Gold

All I need are the boots, baby!
Complete the game

http://www.ps3trophies.com/forums/ps3-trophy-news/4768-puss-boots-trophy-list.html