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