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