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