Here is the full list of all 22 Sword of Asumi achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Saved the World and fell in love #3
Saved the World and fell in love #1
Saved the World and fell in love #4
Killed Mineko at the End
Completed Death of Hikari Ending
Killed Utsuro at the End
Saved the World and fell in love #2
Completed the 'canon' ending to the game
Completed the Dying Alone Ending
Assassinate the kidnappers after they talk
Completed Mercy is for the Weak Ending
Drug the Principal for Information
Skipped the intro on second playthrough
Impress Kami with your poetry skills
Suggest to Kaori she is your type too
Completed Hikari's Unrequited Love Ending
Completed the entire game at least once
Get a perfect score in Tactics with Sen
Try a little cosplay with Kaori
You Spread Rumours about Hiro & Jiro
Came first on the Obstacle Course
Kill Everyone in the intro