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