Here is the full list of all 34 Mitsurugi Kamui Hikae trophies - there are 15 bronze, 14 silver, 4 gold and 1 platinum.
All the trophies unlocked
Clear Easy difficulty
Clear Inferno difficulty
Complete all upgrades
Collect 100,000 SP
Clear Very Hard difficulty
Defeat 1000 enemies
Clear Hard difficulty
Perform 10 Flourishes
Perform 10 Counters
Perform 10 Just Guards
Perform a Counter
Perform a Flourish
Max out Katana Gauge
Clear Normal difficulty
Defeat stage 6 boss "Magatsu Hino Tsurugi"
Defeat stage 5 boss "Magatsu Suzuka"
Defeat stage 4 boss "Magatsu Kaina"
Max out Life Gauge
Defeat stage 3 boss "Suzuka"
Use Zanshin to defeat 100 enemies
Defeat stage 2 boss "Kaiser"
Use Zanshin to defeat 50 enemies
Perform a Just Guard
Defeat 100 enemies
Defeat stage 1 boss "Kaina"
Perform the holy technique "Celestial Judgement"
Defeat 10 enemies
Perform the holy technique "Divine Wind"
Reach "Mitsurugi" zeal level
String 100 hits
String 50 hits
Use Zanshin to defeat an enemy
Watch the tutorial