Here is the full list of all 18 Melon Simulator achievements.
Kill an exploding melon
Play a level from the workshop
Kill 1 Melon
Reach wave 5
Kill 10 melons
Reach wave 10
Reach wave 15
Reach wave 20
Reach wave 25
Kill 100 melons
Kill 200 melons
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