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