Here is the full list of all 66 The Forbidden Arts achievements.
Defeat the Geomancer
Learn the Shield of Fire Ability
Kill 20 Gnolls
Solve the Puzzle in the Abandoned Mines
Kill 10 Assassins
Kill 5 Bears
Collect 1 Phoenix Feather
Clear the Griffin from the Path
Kill 10 Wolves
Kill 20 Assassins
Kill 40 Gnolls
Kill 20 Spiders
Kill 40 Spiders
Defeat the Enchantress
Learn the Roots of Fire Ability
Collect 4 gold in The Green Vale
Collect 4 gold in Black Fang Pass
Collect 10 gold in Korrath Woods
Collect 10 gold in the Abandoned Mines
Collect 10 gold in the Hives
Complete Challenge Tower 1
Complete Challenge Tower 2
Complete Challenge Tower 3
Collect 2 Phoenix Feathers
Collect 3 Phoenix Feathers
Kill 5 Ice Golems
Kill 10 Goblins
Kill 20 Goblins
Kill 40 Goblins
Kill 10 Yetis
Kill 5 Drakes
Collect all 3 fragments of the Dragon's Eye
Collect 4 Phoenix Feathers
Learn the Heat Vision Ability
Defeat the Aeromancer
Collect 4 gold in The Northern Wastes
Collect 10 Gold in The Mountains of Orin
Complete Challenge Tower 4
Kill 10 Frogmen
Kill 20 Frogmen
Kill 40 Frogmen
Kill 5 Minotaurs
Kill 5 Mushrooms
Kill 10 Mushrooms
Collect 5 Phoenix Feathers
Learn the Rain of Fire Ability
Defeat the Hydromancer
Collect 4 gold in the swamp of green mist
Collect 10 gold in the Pools of Murk
Complete Challenge Tower 5
Kill 10 Bandits
Kill 20 Bandits
Kill 5 Harpies
Kill 10 Harpies
Kill 10 Golems
Kill 20 Golems
Kill 10 Snakes
Kill 20 Snakes
Collect 6 Phoenix Feathers
Defeat the Chiromancer
Collect 4 gold in the Desert of Marzule
Collect 10 gold in the Temple of Spirit
Complete Challenge Tower 6
Obtain the Imbued Blades of the Sun
Defeat the Mimic in the Spirit Realm
Defeat the Necromancer