Here is the full list of all 44 Onikira - there are Demon Killer achievements.
You have dodged 50 enemy hits
You have found half of the secret coins
You got the Naginata!
You have completed level The Tengu
You got the Kama Blades!
You have completed level Daimyo's End
You have purchased your first upgrade
You have achieved a 50 hit combo
You have completed Samurai Village
You have defeated the Vanguard
You have found a secret coin
You have found a dragon fragment
You have killed 30 enemies while in the air
You have completed the game
You have purchased all the upgrades
You have completed level Hirumo's Return
You have completed level Earth Clan City
You have completed level Yomi
You have completed level Dragon Showdown
You have all the upgrades
You have defeated the Vanguard without taking damage
You have defeated the Kanabo Oni
You have defeated the Kanabo Oni without taking damage
You got the Tetsubo!
You’ve killed 100 enemies using the Naginata
You’ve killed 100 enemies using the Tetsubo
You’ve killed 100 enemies using the Kama Blades
You have completed a level without taking damage
You gained an SSS rank during combat
You have spent 2500 in the shop
You have upgraded Jiro’s health to maximum
You have found all the secret coins
You have found half of the dragon fragments
You have found all the dragon fragments
You have completed an encounter with a SSS rank
You have achieved a 150 hit combo
You have achieved a 400 hit combo
You have killed 5 enemies using deflected grenades
You have killed 15 enemies using deflected grenades
You have killed 30 enemies using deflected grenades
You have started the game again after completing it once.
You have killed 10 consecutive enemies while in the air
(Jump off the cliff onto the clouds)
You have played for over 2 hours!