Here is the full list of all 16 Artificer's Tower achievements.
Defeat the Bugbear Shaman
Get any skill to Adept (200) with a mage
Promote 25 students to Mages in one tower
Build 100 active rooms in one tower
Have 30 students all with 100% happiness in one tower
Train a student to the maximum potential Guru (300)
Let erratic essence hang out for 9+ hours
Fill the council with mages who started as students
Get a Grandmaster level mage to 100% happiness
Promote a mage to Archmage
Unlock all research
Have a mage survive the GodMaker
Defeat Troll Shaman
Defeat the Necromancer
Last to day 100 on Survival mode
Hire an Archmage from the Portal