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