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