Here is the full list of all 10 Monster Harvest trophies - there are 8 bronze and 2 gold.
Begin your first day on the farm.
Recieve a Planimal from the Professor.
Repair the bridge to the rec center.
Unlock the furniture shop.
Unlock the fishing rod.
Defeat the queen.
Defeat Rigley.
Apply red slime to a crop.
Apply green slime to a crop.
Apply blue slime to a crop.