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