Here is the full list of all 87 Arcanium: Rise of Akhan achievements.
Reach level 20 with Mozebus
Defeat 20 Bosses in the Arena
Reach level 20 with Drakkaw
Choose 50 Neutral Nature Ability cards from Battle rewards
Choose 50 Neutral Arcana Ability cards from Battle rewards
Choose 50 Neutral Light Ability cards from Battle rewards
Reach level 20 with Maverick
Reach level 20 with Ragnarok
Choose 50 Neutral Elemental Ability cards from Battle rewards
Choose 50 Neutral Void Ability cards from Battle rewards
Unlock 100% of Uzir
Unlock 100% of Scorched Lands
Purchase 50 Artifacts from Forges
Visit 25 Shrines in Anador
Unlock 100% of Anador
Reach level 20 with Lazaar
Purchase 50 Minions from Outposts
Purchase 50 Items from Alchemists
Reach level 20 with Thoram
Visit 25 Shrines in Scorched Lands
Visit 25 Shrines in Uzir
Reach level 20 with Milady
Reach level 20 with Aurora
Unlock 75% of Anador
Reach level 20 with Leon
Unlock 75% of Scorched Lands
Unlock 75% of Uzir
Reach level 20 with Misty
Use Campsites 50 times
Upgrade 100 Abilities
Reach level 20 with Celeste
Visit 50 Oracles
Reach account Mastery level 200
Reach level 20 with Carrion
Reach level 20 with Tara
Reach level 20 with Shinzo
Unlock 50% of Anador
Unlock 50% of Uzir
Use the Inn 50 times
Spend 9999 Gold or more on Healing during an Arena run
Spend 5,000 Gold at any Trainer
Reach account Mastery level 150
Spend 5,000 Gold at any Forge
Defeat Akhan in Apex mode
Unlock 50% of Scorched Lands
Reach Cataclysm 25 times
Purchase 50 Abilities from Trainers
Reach level 20 with Bjorn
Spend 9999 Gold at the Quartermaster during an Arena run
Reach level 20 with Angorn
Defeat Akhan in Mythic mode
Unlock 25% of Uzir
Defeat Akhan in Heroic mode
Unlock 25% of Scorched Lands
Defeat Akhan in Challenger mode
Defeat Noctus once in any difficulty
Reach account Mastery level 100
Unlock 25% of Anador
Win an Arena run with a total of 10 Injuries or more on your Heroes
Spend 9999 Gold or more on Perks during an Arena run
Defeat a Boss with only 1 Hero standing
Defeat Sparks in the Arena
Select 5 or more Fate cards during an Arena run
Defeat Akhan in Expert mode
Activate 50 unique tiles in Uzir
Defeat 50 Uzir enemies
Defeat 50 Scorched Lands enemies
Destroy 6 or more Corrupted enemies during an Arena run
Obtain 6 Injuries or more on a Hero in the Arena
Reach account Mastery level 50
Select 3 or more Hazardous Battles during an Arena run
Defeat Ogar in the Arena
Win an Arena run without receiving any Injury
Defeat Hemlock in the Arena
Play 1 Arena game
Defeat Ra'Kzar once in any difficulty
Gain a total of 100 Essence
Activate 50 unique tiles in Scorched Lands
Defeat Akhan in Hard mode
Defeat 50 Anador enemies
Activate 50 unique tiles in Anador
Defeat Aranax once in any difficulty
Defeat Akhan in Normal mode
Defeat Akhan once in any difficulty
Reach Master 50 to unlock Arena mode
Destroy 3 enemies in one Turn
Destroy 2 enemies in one Turn