Here is the full list of all 12 Low Magic Age achievements.
Won 1000 battles in the Arena
Got a character to level 10
Won 1000 battles in the Arena without defeat
Won 100 battles in the Arena
Won 100 battles in the Arena without defeat
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
Got a character to level 20
Got a character to level 40