Konan needs prep for 600 billion tags unless you start her off with them. Either way, I say Mangetsu just reforms into himself. He's made of water so he can come back from any explosion or damage. Konan is also loggia type, however, and can fly in any case. This is almost a stalemate, unless Mangetsu can use Samehada to steal her chakra-- then she's done.
mangetsu wouldnt probably die even if konan brought her trap. suigetsu survived point blank bijuudama. and konan fans beg to differ about the "top tier" comment lol. anyhow i think konan loses if mangetsu has his swords