Here is the full list of all 27 Siege Wars achievements.
Complete 50 levels for 3 stars
Complete all levels in Citadel location
Assassinate White Mage
Make away with Violet Mage
Upgrade your Catapult weapon up to level 8
Complete all levels in Volcano location
Cast Earthquake spell
Destroy Fire Mage
End the life of Volcano Mage
Complete all levels in Icy Plains location
Liquidate Sky Mage
Slay Frost Mage
Complete all levels in Black Marsh location
Brush of Black Mage
Complete 25 levels for 2 stars or more
Cast Heal spell
Get rid of Green Mage
Complete all levels in Wastelands location
Complete 10 levels for 1 star or more
Defeat Yellow Mage
Cast Shield spell
Get magic amulet from a level
Complete one level with any score
Kill an enemy from Sand Mage Guild
Upgrade your Bombard weapon up to level 8
Upgrade your Ballista weapon up to level 8
Upgrade your Arch-Ballista up to level 8