Here is the full list of all 59 Lichdom: Battlemage achievements.
Complete any Vortex Portal
Some people just want to watch the world burn
Complete 20 Loot Machines
Back from the grave
Soddentrod is a memory
Destroy more than 20 special crates in Soddentrod
Oops, did I break that crate on you?
Careful with the crates in Soddentrod
At what cost
Defeat the Ancient Golem
Defeat the Ancient Golem on Battlemage Difficulty
Zasad water source restored
Complete 10 Loot Machines
Maelstrom's secrets revealed
Defeat Frostclaw
Defeat Frostclaw on Battlemage Difficulty
Destroy 20 Loot Crystals
Complete 6 Loot Machines
Find 20 Loot Orbs
Rogiro and his undead beast are no more
Defeat Rogiro and his Undead Hulk on Battlemage Difficulty
Destroy 20 Loot Spores
Complete 2 Loot Machines
Craft your first spell
Choose your first sigil
Level your Fire Sigil to 16
Level your Ice Sigil to 16
Level your Lightning Sigil to 16
Level your Corruption Sigil to 16
Level your Necromancy Sigil to 16
Level your Delirium Sigil to 16
Level your Kinesis Sigil to 16
Level your Phase Sigil to 16
Find all of the Plaques in Old Drivasser
Find all of the Plaques in the Grey Teeth
Find all of the Plaques in the Maelstrom
Find all of the Plaques in Zasad
Find all of the Plaques in Lost Zasad
Find all of the Plaques in Soddentrod
Find all of the Plaques in the Sinkhole
Find all of the Plaques in Drivasser
Complete all Skirmish Portals
Complete an entire New Game Plus sequence
Complete all Hunt Portals
Complete all Disable Portals
Complete three sets of Vortex Portals
Complete an entire series of Vortex Portals in one sitting
Fall in the lava in the Maelstrom
Equip nine unique spells
Craft a Spell with a Unique Pattern and 4 Legendary Augments
Defeat the Ancient Golem on Badass Difficulty
Defeat Frostclaw on Badass Difficulty
Defeat Rogiro and his Undead Hulk on Badass Difficulty
Equip all tier 20 spells
Craft every available synergy spell