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