Here is the full list of all 23 Duck Season achievements.
Dog
Set the table for dinner
Beat All Cartridge Games
Its over, you lose
Tried to get Mom's attention
Hit the baseball with the bat into the kitchen
Cannon Ending
What time is it really?
Shot the sun with the golden shell
Don't shoot the dog in any playthrough
A better game
Platoon ending
Shoot all the cattails in the game world
Shoot the sitting duck in the duck world
Watch all the VHS tapes
Use the Kid Wizard Book
Stuck forever
Throw something out the window
Kill 100 Ducks
Flip the sign in the game world
Kill two ducks with one shot
Shoot the dog more than once in a playthrough