Here is the full list of all 44 Mage Tower achievements.
reach attack 100
enter the forest camp
first shop
first composite
defeat chaos demon
reach level 100
save Ramir
kill Nydigov
use skill in battle
use skill to recover health
first outfit
unlock all equipment slot
a partner joins the team
reach attack 200
reach attack 500
reach attack 1000
reach kill 1000
reach kill 2500
reach kill 5000
reach kill 10000
reach kill 20000
defeat golem
defeat minotaur
reach level 200
reach level 500
clean all monsters of wasterland I
clean all monsters of wasterland II
wasteland I uses less than 15 health potions
wasteland II uses less than 15 health potions
wasteland III uses less than 8 health potions
In wasterland I, less than 5 kills with NPC assistance
In wasterland II, less than 5 kills with NPC assistance
In wasterland III, less than 5 kills with NPC assistance
defeat dark samurai
defeat fire mage
defeat dark mage
defeat lady samurai
defeat executioner
defeat black knight
enter Watch Fortress
defeat banshee
defeat the unicorn demon
defeat the scorpion king
exchange health potion