Okay so Nyan has the ap advantage. Still going for Shantae though. Pike Balls/Scimitars can harm him if he goes for close combat. His air manipulation might not be considered a projectile, however Shantae should still he able to teleport away from them. If Nyan harms her too much then Super Revive Dance fully heals her. Monster Milk might be able to counter the ap difference.
Shantae's gonna be hard pressed to hit him. I feel like she's gonna need the explosion dance to actually deal with him. I still say Shantae takes this with high difficulty. Her explosion and healing dances are her best tools here with most everything else kinda useless.