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