Here is the full list of all 35 Akai Katana Shin achievements.
Summon your guardian
Defeat the Fujiibara attack cruiser
Defeat 1st stage boss Hiiragi
Defeat the Goura M76 heavy tank in stage 2
Defeat 2nd stage boss Shumeigiku
Defeat the Gaimon tank in stage 3
Defeat 3rd stage boss Shakunage
Defeat the Arakashi submarine in stage 4
Defeat 4th stage boss War Demon Hiiragi
Defeat the Inuenju helicopter, mid-boss in stage 5
Defeat 5th stage boss Nazuna
Defeat the Himeshara heavy attack helicopter
Defeat Ayame & Ran
Defeat final boss Emperor Bashou
Complete the game with the type 1 Shakevolt
Complete the game with the type 2 Shakevolt
Complete the game with the type 3 Shakevolt
Complete the game using the type 1 Shakevolt without continuing
Complete the game using the type 2 Shakevolt without continuing
Complete the game using the type 3 Shakevolt without continuing
Earn 100 000 000 points
Earn 200 000 000 points
Earn 300 000 000 points
Do a 128 hit combo
Do a 256 hit combo
Earn 400 000 000 points
Earn 600 000 000 points
Earn 800 000 000 points
Do a 3 000 hit combo
Do a 6000 hit combo
Do a 9 999 hit combo
Watch the true ending