Here is the full list of all 45 Conan Chop Chop achievements.
Complete the tutorial
Obtain Conan's Barbarian Rage
Obtain Valeria's Tornado Slash
Obtain Belit's Rain of Arrows
Obtain Pallantides' Roar of the Dragon
Obtain 1 trait for Conan
Obtain 1 trait for Valeria
Obtain 1 trait for Belit
Obtain 1 trait for Pallantides
Obtain 3 traits for Conan
Obtain 3 traits for Valeria
Obtain 3 traits for Belit
Obtain 3 traits for Pallantides
Forge a Weapon at the Blacksmith in your Town
Forge a Shield at the Blacksmith in your Town
Forge an Armor at the Blacksmith in your Town
Forge a Charm at the Blacksmith in your Town
Defeat a miniboss in Nemedia
Defeat a miniboss in Darkwood
Defeat a miniboss in Koth
Defeat a miniboss in Vanaheim
Defeat a miniboss in Hyperborea
Defeat Thak
Defeat the Sand Worm
Defeat the Frost Giant
Defeat Skelos
Wear a matching Shield and Armor set
Have 3 pets at once
Open a Gold Chest in the world
Find and return the Doll
Use Oasis Key
Locate the Staff of Epemitreus
Return the Staff of Epemitreus
Equip 4 Charms
Defeat Xaltotun as Conan
Defeat Xaltotun as Valeria
Defeat Xaltotun as Belit
Defeat Xaltotun as Pallantides
Restored the Shield Shop in your Town
Restored the Weapon Shop in your Town
Restored the Armor Shop in your Town
Restored the Charm Shop in your Town
Restored your Town
Defeat Thoth-Amon
Earn all achievements in 'Conan Chop Chop'