Here is the full list of all 21 Plants vs. Zombies GOTY Edition achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Grow the Tree of Wisdom to 100 feet
Get to 20 flags in Survival Endless
Discover the top secret zombie
Collect all 49 plants
Defeat 2 Gargantuars with Corn Cob missiles in a single level.
Complete a daytime pool level without using pea shooters of any kind.
Get to a streak of 15 in Vasebreaker Endless
Get to a streak of 10 in I, Zombie Endless
Beat all 20 mini games.
Enable Mustache Mode
Complete a nighttime level without planting any Mushrooms.
Complete a daytime level by planting only Mushrooms and Coffee Beans.
Defeat a normal roof level without using any catapult plants.
Hypnotize the lead dancer zombie
Bowl over 5 zombies with a single Wall-Nut.
Get 8000 sun during a single level.
Pick up 30 coins in a row on a single level without letting any disappear.
Get the golden sunflower trophy
Complete adventure mode
Blow up a zombie using a potato mine
Blow up 10 zombies with a single cherry bomb