Here is the full list of all 9 Noxious Weeds Demo achievements.
Lose 5 times
Harvest 30 Trees
Defeat 1000 Sprouts
Defeat a Pepper-Oni
Defeat the corn
Defeat 200 Owlnions
Defeat 1000 Currants
Clear the Spring Scenario with Orchardist
Hold 600 water units at the end of a wave