Here is the full list of all 12 Low Magic Age achievements.
Got a character to level 40
Won 100 battles in the Arena without defeat
Won 100 battles in the Arena
Got a character to level 20
Got a character to level 10
Won 10 battles in the Arena
Won 10 battles in the Arena without defeat
Got a character to level 2
Won a battle in the Arena
The first time you entered this low-magic world
Won 1000 battles in the Arena
Won 1000 battles in the Arena without defeat