Here is the full list of all 17 My Singing Monsters trophies - there are 17 bronze.
Get Cold Island
Get a 4 element monster
Get all Plant Island monsters
Clear all Obstacles on an Island
Get a monster 100% happy
Get 3 element Monster
Reach level 10
Breed a monster
Get a Monster
Get a level 15 Monster
Get all Cold Island Monsters
Get Air Island
Get all Air Island Monsters
Get Water Island
Get all Water Island Monsters
Get Earth Island
Get all Earth Island Monsters