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 #1
Killed Utsuro at the End
Saved the World and fell in love #2
Drug the Principal for Information
Came first on the Obstacle Course
Skipped the intro on second playthrough
Killed Mineko at the End
Saved the World and fell in love #4
Saved the World and fell in love #3
Completed Death of Hikari Ending
Completed the 'canon' ending to the game
Completed Hikari's Unrequited Love Ending
Assassinate the kidnappers after they talk
Completed Mercy is for the Weak Ending
Completed the Dying Alone Ending
Completed the entire game at least once
Try a little cosplay with Kaori
Suggest to Kaori she is your type too
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