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