There are 12 Trophies that can be collected.

Bronze

Smarty Branches
Grow the Tree of Wisdom to at least 100 feet

Crash of the Titan
Defeat your first Gargantuar

ZFF's 4 Evr
Bowl a winner with a friend in Co-Op Wall-Nut Bowling

Soil Your Plants
Plant your first 10 peashooters

Explodonator
Blast 10 zombies at once with a Cherry Bomb!

Close Shave
Survive the zombie onslaught after all lawnmowers have been used

Shopaholic
Go trunk diving and spend at least $25,000 on Crazy Dave's Twiddydinkies

Silver

Master of Morticulture
Collect all 49 plants in the game

Alive and Planting
Survive 40 waves of pure zombie ferocity

Versus vs Versus
Go on a 5 game winning streak in VS. mode

Nom Nom Nom
Stop the horde using only the Sunflower, Wall-Nut, and Chomper on any level

Gold

Home Lawn Security
Complete adventure mode

http://www.ps3trophies.org/game/plants-vs-zombies/trophies/