Here is the full list of all 14 Duckpocalypse achievements.
Shoot 1984 ducks.
Get a score of 20k or higher.
Cut down 20 trees.
Shoot and miss 30 times in a row.
Kill 50 biker ducks.
Get a score of 15k or higher.
Harm no trees a whole game.
Get a score of 25k or higher.
Kill 15 ducks with 1 barrel explosion.
Kill 50 leviathan ducks.
Kill 15 ducks with an exploding car.