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