The Genma are monstrosities from the underworld. According to the official PlayStation description, the Malice surrounding Kyoto brings these fiends into the world of the living, where their atrocities plunge the capital into dread.
Musashi's answer is the Oni Gauntlet, a mystical artifact that grants power beyond human limits. Besides helping him cut down Genma, it can absorb Genma souls and convert them into a power source to enhance its wearer.
The official page does not yet explain the full upgrade tree, soul economy or every Genma type. Those details belong in a tested mechanics update once the released game provides them.