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.
Complete adventure mode
Hypnotize the lead dancer zombie
Complete a daytime pool level without using pea shooters of any kind.
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 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 10 in I, Zombie Endless
Get to a streak of 15 in Vasebreaker Endless
Get to 20 flags in Survival Endless
Collect all 49 plants
Grow the Tree of Wisdom to 100 feet
Discover the top secret zombie
Enable Mustache Mode
Defeat a normal roof level without using any catapult plants.
Get 8000 sun during a single level.
Defeat 2 Gargantuars with Corn Cob missiles in a single level.
Complete a daytime level by planting only Mushrooms and Coffee Beans.
Complete a nighttime level without planting any Mushrooms.
Beat all 20 mini games.