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