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