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