Here is the full list of all 31 Barbearian achievements.
Walk 10k
Reach maximum chain (999)
Completed all quests at Skeletal Park
Reach 500 chain
Collect a total of 25k loot
Swing your axe 1k times
Complete the first quest
Free your first minion
Collect a total of 250k loot
Take down 50k enemies
Fire a weapon pickup 1k times
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 Corrupted Forest
Completed all quests at Valley of Bones
Completed all quests at Strange Machinations
Compeleted all special quests
First Master Class completed
Complete all Master Classes
Defeat Megaskull
Defeat The Absorber
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