Well the green poe wont appear like the others. Have you been in a room with a picture of the green poe on the wall? If you have you need to shoot it with the Bow and solve a jigsaw puzzle.
Once you do that the center room will have a cut scene where the purple poe appears and you have to fight her. To defeat the green one use the same meathod you did with the blue and red ones (can't remember their names). To defeat the purple one you need to wait for the 4 clones to appear and shoot the one that spins around.