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