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
Get the golden sunflower trophy
Get to a streak of 10 in I, Zombie Endless
Defeat 2 Gargantuars with Corn Cob missiles in a single level.
Defeat a normal roof level without using any catapult plants.
Discover the top secret zombie
Enable Mustache Mode
Collect all 49 plants
Get to a streak of 15 in Vasebreaker Endless
Complete a daytime pool level without using pea shooters of any kind.
Get 8000 sun during a single level.
Complete a nighttime level without planting any Mushrooms.
Complete a daytime level by planting only Mushrooms and Coffee Beans.
Beat all 20 mini games.
Blow up 10 zombies with a single cherry bomb
Complete adventure mode
Hypnotize the lead dancer zombie
Bowl over 5 zombies with a single Wall-Nut.
Pick up 30 coins in a row on a single level without letting any disappear.
Blow up a zombie using a potato mine