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