Here is the full list of all 18 Melon Simulator achievements.
Reach wave 10
Kill 200 melons
Reach wave 5
Kill 100 melons
Kill 10 melons
Kill an exploding melon
Kill 1 Melon
Play a level from the workshop
Reach wave 15
Reach wave 20
Reach wave 25
Kill 500 melons
Kill 1000 melons
Kill 2000 melons
Publish a level to the workshop
Open a level in the editor
Save a level in the editor
Reach wave 30