Here is the full list of all 10 Monster Harvest achievements.
Apply green slime to a crop.
Recieve a Planimal from the Professor.
Apply red slime to a crop.
Begin your first day on the farm.
Repair the bridge to the rec center.
Unlock the furniture shop.
Unlock the fishing rod.
Defeat the queen.
Defeat Rigley.
Apply blue slime to a crop.