Here is the full list of all 16 Mina & Michi achievements.
Defeat the third Boss.
Solve 25 puzzles.
Open 10 treasure chests.
Defeat 150 enemies.
Defeat the second Boss.
Defeat 100 enemies.
Solve 10 puzzles.
Open 5 treasure chests.
Defeat 50 enemies.
Defeat the first Boss.
Defeat 25 enemies.
Solve 5 puzzles.
Open 1 treasure chest.
Get 100 gems.
Get 50 gems.
Get 25 gems.