Here is the full list of all 59 Lichdom: Battlemage achievements.
Complete 20 Loot Machines
Find all of the Plaques in the Grey Teeth
Defeat Rogiro and his Undead Hulk on Badass Difficulty
Find all of the Plaques in Old Drivasser
Defeat Rogiro and his Undead Hulk on Battlemage Difficulty
Complete 10 Loot Machines
Maelstrom's secrets revealed
Defeat Frostclaw
Complete 6 Loot Machines
Destroy 20 Loot Crystals
Find 20 Loot Orbs
Rogiro and his undead beast are no more
Complete 2 Loot Machines
Destroy 20 Loot Spores
Craft your first spell
Choose your first sigil
Zasad water source restored
At what cost
Soddentrod is a memory
Back from the grave
Some people just want to watch the world burn
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 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 any Vortex Portal
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
Careful with the crates in Soddentrod
Destroy more than 20 special crates in Soddentrod
Defeat the Ancient Golem
Equip nine unique spells
Craft a Spell with a Unique Pattern and 4 Legendary Augments
Defeat the Ancient Golem on Badass Difficulty
Defeat the Ancient Golem on Battlemage Difficulty
Defeat Frostclaw on Badass Difficulty
Defeat Frostclaw on Battlemage Difficulty
Equip all tier 20 spells
Craft every available synergy spell
Oops, did I break that crate on you?