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