Here is the full list of all 31 Monsters and Medicine achievements.
See all 6 types of monsters.
Finish all 8 tutorial levels.
Beat the final level.
Beat all optional puzzle levels.
Discover the Haunted Forest.
Discover Fuzzy Isle.
Discover Ghost Island.
Discover Swamp Town.
Discover Lava Land.
Discover the Mutant Mountains.
Cure 8 monsters in a single turn.
Cure 12 monsters in a single turn.
Beat a random level without ever having more than 4 wards.
Beat a random level without placing any rooms other than wards.
Beat a random level with exactly one death.
Beat a random level without any monsters dying.
Beat a random level with exactly one death from losing.
Beat 10 random levels.
Beat 100 random levels.
Cure 50 monsters in total.
Cure 200 monsters in total.
Cure 1000 monsters in total.
Cure 10000 monsters in total.
Have a monster skip past 8 waiting monsters and continue to beat the level.
Have 12 monsters near death outside your hospital at once and continue to beat the level.
Beat a random level with a ward at maximum capacity and cure rate.
Cause 8 more monsters to enter your hospital than was predicted.
Lose a level without curing any monsters.
Build 10 rooms in total
Build 100 rooms in total
Build 500 rooms in total