Here is the full list of all 54 Monster Crawl achievements.
Reach level 10 with Warrior
Reach level 12 with Ranger
Reach level 15 with Wizard
Reach level 15 with Blademaster
Complete your first dungeon
Kill monsters
Destroy monster Generators
Reach depth 7
Reach depth 12
Reach depth 15
Use keys to open doors
Equip different relics
Complete Challenges
Visit Relic rooms and open the boxes
Explode bombs
Perform Critical hits with any attack
Killed giant monsters
Make Death even more DEAD
Monster fell in a hole
Died due to a bomb exploding
Complete Crawls
Complete a Crawl with 5 Heroes
Cooldown and eat donuts
Always time for a snack
Collect the shiny
Find maps in the dungeon
Magic in a bottle
Gain maximum Health upgrades
Gain maximum Damage upgrades
Gain maximum XP upgrades
Gain maximum Critical Chance upgrades
Gain maximum Area Effect upgrades
Gain maximum Cooldown upgrades
Gain maximum Duration upgrades
Gain maximum Luck upgrades
Gain maximum Range upgrades
Defeat the Rat King
Defeat Bone Lord
Defeat Mama Grunt
Defeat Grom
Defeat Ultimate Death
Defeat 5 bosses