It is not such a costume. It is a sheet with 2 holes at the eyes. But the effects are made by magic tricks. The transparency effect, and passing through walls are done with the help of a video projector and a mirror. The flying trick is made with ropes(thin ones) like in magic. The Phantom was Bluestone, The Great, an Ex-Magician wanted in several states! The phantom pretended to be The Phantom of Vasquez the Pirate.
He was faking the Phantom to scare turists away from the Haunted Island so he can search for Vasques' treasure.