Here is the full list of all 14 Miss Neko: Pirates achievements.
Captain, embark on your journey of revenge!
Freed Seraphina
Freed Isabella
Complete the seaside level
Complete the mine cave level
Complete the fortress level
Astaria is pleased with you
Collect all the figurines in level 1
Collect all the figurines in level 2
Collect all the figurines in level 3
Defeat Jade who has not been weakened
Defeat Lumi who has not been weakened
Defeat Mariyn who has not been weakened
Defeat Yala who has not been weakened