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