Here is the full list of all 43 Plants vs. Zombies trophies - there are 28 bronze, 12 silver, 2 gold and 1 platinum.
Build 5 Cob Cannons in a single level.
Stop the horde using only the Sunflower, Wall-Nut, and Chomper on any level
Complete ZomBotany without using Wall-nuts, Tall-nuts or Pumpkins.
Complete a level using only explosive plants to kill zombies.
Complete a daytime level by planting only Mushrooms and Coffee Beans.
Complete Adventure mode a second time.
Discover the Yeti zombie.
Collect all 49 plants in the game
Immobilize 20 full-sized zombies with a single Ice-shroom.
Plant a Winter Melon on every lane.
Complete Last Stand with 2,000 sun remaining
Beat all 20 mini games
Complete Pogo Party without using Tall-Nuts or Magnet-shrooms
Grow 10 Zen Garden plants to full size
Complete a daytime pool level without using Pea-shooters of any kind.
Complete Column Like You See'em without using Jalapenos
Kill 10 zombies with a single lawn mower.
Crush 5 zombies with a single Squash.
Feel the rhythm, feel the rhyme, you've one level to destroy 3 bobsleds, it's Jalapeno time!
Accumulate 8,000 sun during a single level.
Keep 10 Twin Sunflowers alive in a single level.
Upgrade all your plants in Beghouled
Get 3 of a kind in Slot Machine
Bowl over 5 zombies with a single Wall-nut.
Go trunk diving and spend at least $25,000 on Crazy Dave's Twiddydinkies
Complete adventure mode
Defeat your first Gargantuar
Defeat a normal roof level without using any Catapult plants.
Pick up 30 coins in a row on a single level without letting any disappear.
Complete a nighttime level without planting any Mushrooms.
Complete an extremely foggy level without using Planterns or Blovers.
Complete a pool level without using water plants.
Blast 10 zombies at once with a Cherry Bomb!
Defeat the last zombie in a level with a lawn mower.
Blow up a zombie using a Potato Mine.
Survive the zombie onslaught after all lawnmowers have been used
Plant your first 10 peashooters
You've won every trophy, climbed every mountain, defeated every zombie, planted every plant. Congratulations!
Grow the Tree of Wisdom to at least 100 feet
Survive 40 waves of pure zombie ferocity
Defeat 2 Gargantuars with Corn Cob missiles in a single level.
Collect all Zen Garden, Mushroom Garden and Aquarium Garden plants
Complete Seeing Stars before the first Flag Zombie appears