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
Clear Easy difficulty
Clear Normal difficulty
Defeat stage 6 boss "Magatsu Hino Tsurugi" (any difficulty)
Complete all upgrades
Max out Life Gauge
Max out Katana Gauge
Defeat stage 5 boss "Magatsu Suzuka" (any difficulty)
Defeat 1000 enemies
Defeat stage 4 boss "Magatsu Kaina" (any difficulty)
Use Zanshin to defeat 100 enemies
Perform 10 Just Guards
Perform 10 Flourishes
Defeat stage 3 boss "Suzuka" (any difficulty)
Use Zanshin to defeat 50 enemies
Perform 10 Counters
Defeat stage 2 boss "Kaiser" (any difficulty)
Defeat 100 enemies
Perform a Counter
Perform a Just Guard
Perform a Flourish
Watch the tutorial
Defeat stage 1 boss "Kaina" (any difficulty)
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"
Reach "Mitsurugi" zeal level