Here is the full list of all 34 Monstermonger achievements.
Completed your first day in the Moonlit Forest
Completed your second day in the Jungle Ruins
Completed your third day in the Forgotten Crypt
Completed your fourth day in the Endless Desert
Completed your fifth day in the Misty Shores
Completed your sixth day in the Ancient Swamp
Completed your seventh day in the Abandoned Mine
Completed your eighth day in the Smoldering Void
Reached Apprentice level
Reached Adventurer level
Reached Hunter level
Reached Wholesaler level
Reached Monstermonger level
Win your first freeplay hunt (Singleplayer or Multiplayer)
Win 5 freeplay hunts (Singleplayer or Multiplayer)
Win 10 freeplay hunts (Singleplayer or Multiplayer)
Win 50 freeplay hunts (Singleplayer or Multiplayer)
Win 100 freeplay hunts (Singleplayer or Multiplayer)
Win a freeplay hunt by the narrowest margin
Make two turns in a row by leaving your opponent no valid moves
Win a freeplay hunt against every AI difficulty
Win a hunt by forcing stalemate
Win a freeplay hunt ending with only magical villagers in the team
Complete all bestiaries
Win a hunt with a team skill level of 9 of each type
Captured all monsters in the Moonlit Forest
Captured all monsters in the Jungle Ruins
Captured all monsters in the Forgotten Crypt
Captured all monsters in the Endless Desert
Captured all monsters in the Misty Shores
Captured all monsters in the Ancient Swamp
Captured all monsters in the Abandoned Mine
Captured all monsters in the Smoldering Void
Win a freeplay hunt vs monstermonger AI without a starting bonus skill