Here is the full list of all 40 Lichdom Battlemage trophies - there are 29 bronze, 5 silver, 5 gold and 1 platinum.
Complete any Vortex Portal
Finish the Game
Finish the game on Battlemage difficulty
Complete Soddentrod Chapter
Back from the grave on Battlemage difficulty
Back from the grave
Blow up a crate, when an enemy is standing next to it
Destroy the crates in Soddentrod
Sacrifice at Zasad
Defeat the Ancient Golem
Defeat the Ancient Golem on Battlemage Difficulty
Zasad water source restored
Maelstrom's secrets revealed
Defeat Frostclaw
Defeat Frostclaw on Battlemage Difficulty
Craft your first spell
Fall in the lava in the Maelstrom
Rogiro and his undead beast are no more
Defeat Rogiro and his Undead Hulk on Battlemage Difficulty
Choose your first sigil
Unlock all the Lichdom Battlemage Trophies
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
Equip nine unique spells
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
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
Finish the game on Badass difficulty
Back from the grave on Badass difficulty