Here is the full list of all 34 Magic Research 2 achievements.
Complete the Training Towers.
Defeated the Headmaster of the School.
Defeat Lytha, Doom Sorceress.
Complete the game by defeating Satell.
Complete the game by defeating your closest companion.
Save the World from the deadly disease.
Complete the Universal Challenge.
Defeat the Creator.
Complete the Training Towers within 5 minutes of starting a run.
Unlock "Synchro".
Find the Boosting Lamp.
Unlock "Familiars".
Build an item combination machine.
Build a Spellcrafting Furnace.
Unlock "Rituals".
Finally, finally, own the land your home is built on.
Become free from the limitations of needing land to build on.
Learn all that there is to learn about an Element.
Fully unlock the Poison element.
Fully unlock the Mind element.
Fully unlock the Life element.
Fully unlock the Electric element.
Fully unlock the Death element.
Fully unlock the Holy element.
Fully unlock the Time element.
Fully unlock the Space element.
Complete the game while under the effects of the Pouchless challenge. You can do it without an item pouch!
Complete the game while under the effects of the Timed challenge. Your damage output is through the roof!
Complete the game while under the effects of the Danger challenge. Crazy-high numbers cannot stop you!
Complete the game while under the effects of the Unskilled challenge. Your Rank spell power bonuses were not needed!
Complete the game while under the effects of the Primary challenge. It turns out you don't need all the Elements!
Unlock "Exploration".
Retire for the first time.
Complete every Storyline in the game.