Here is the full list of all 31 Barbearian achievements.
First Master Class completed
Defeat Ancient Mechanism
Completed all quests at Valley of Bones
Collect a total of 250k loot
Take down 50k enemies
Fire a weapon pickup 1k times
Defeat The Absorber
First memory unlocked
Completed all quests at Corrupted Forest
Defeat Megaskull
Completed all quests at Skeletal Park
Walk 10k
Reach 500 chain
Collect a total of 25k loot
Swing your axe 1k times
Complete the first quest
Free your first minion
Reach maximum chain (999)
Rescue all trapped minions
Unlock all weapon pickups
All memories unlocked
Wasted perfectly good loot on some boxes
Completed all quests at Strange Machinations
Compeleted all special quests
Complete all Master Classes
Defeat Moo Mobile
Defeat Master Arbitrator
Defeat Meta Engine
Defeat the rhyme blaster, the only true lyrical master
Complete the game
Complete the game with 100% completion rating