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