Here is the full list of all 40 Lichdom Battlemage trophies - there are 29 bronze, 5 silver, 5 gold and 1 platinum.
Unlock all the Lichdom Battlemage Trophies
Level your Necromancy Sigil to 16
Level your Lightning Sigil to 16
Level your Delirium Sigil to 16
Maelstrom's secrets revealed
Level your Corruption Sigil to 16
Level your Phase Sigil to 16
Craft every available synergy spell
Level your Ice Sigil to 16
Equip all tier 20 spells
Equip nine unique spells
Level your Kinesis Sigil to 16
Level your Fire Sigil to 16
Craft a Spell with a Unique Pattern and 4 Legendary Augments
Complete an entire New Game Plus sequence
Complete an entire series of Vortex Portals in one sitting
Complete any Vortex Portal
Finish the game on Badass difficulty
Finish the game on Battlemage difficulty
Finish the Game
Back from the grave on Badass difficulty
Back from the grave on Battlemage difficulty
Complete Soddentrod Chapter
Back from the grave
Destroy the crates in Soddentrod
Blow up a crate, when an enemy is standing next to it
Defeat Rogiro and his Undead Hulk on Badass Difficulty
Sacrifice at Zasad
Defeat the Ancient Golem
Defeat the Ancient Golem on Badass Difficulty
Defeat the Ancient Golem on Battlemage Difficulty
Zasad water source restored
Defeat Frostclaw on Badass Difficulty
Fall in the lava in the Maelstrom
Defeat Frostclaw
Defeat Frostclaw on Battlemage Difficulty
Craft your first spell
Rogiro and his undead beast are no more
Defeat Rogiro and his Undead Hulk on Battlemage Difficulty
Choose your first sigil