Here is the full list of all 14 Militia achievements.
Finish the Dark World Tutorials
Clear a floor in a single turn
Clear a floor with a single unit left
Finish the Light World Tutorials
Win the first tutorial match
Reach Rank 10 in Dark World Mode
Win 10 Matches of Militia
Win 50 Matches of Militia
Win 100 Matches of Militia
Win a match with a single unit left
Destroy 7 enemy units in a single turn
Win a practice match
Win 5 Matches in a Row
Reach Rank 10 in Light World mode