Here is the full list of all 33 Mitsurugi Kamui Hikae achievements. It takes around 8-10 hours to unlock all of the achievements on Windows.
Clear Very Hard difficulty
Complete all upgrades
Clear Hard difficulty
Collect 100,000 SP
Clear Inferno difficulty
Perform 10 Flourishes
Perform a Counter
Perform 10 Counters
Use Zanshin to defeat 100 enemies
Perform 10 Just Guards
Clear Normal difficulty
Perform a Just Guard
Use Zanshin to defeat 50 enemies
Perform a Flourish
Max out Katana Gauge
Watch the tutorial
Defeat 1000 enemies
Perform the holy technique "Celestial Judgement"
Perform the holy technique "Divine Wind"
Max out Life Gauge
Clear Easy difficulty
Defeat stage 5 boss "Magatsu Suzuka" (any difficulty)
Defeat stage 6 boss "Magatsu Hino Tsurugi" (any difficulty)
Defeat stage 1 boss "Kaina" (any difficulty)
Defeat stage 2 boss "Kaiser" (any difficulty)
Defeat stage 3 boss "Suzuka" (any difficulty)
Defeat stage 4 boss "Magatsu Kaina" (any difficulty)
Defeat 10 enemies
Defeat 100 enemies
Use Zanshin to defeat an enemy
String 50 hits
String 100 hits
Reach "Mitsurugi" zeal level