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