i mostly turtle at the opposite side of the screen to her and wall jump until she stops raising her sword to do another blade beam, though i do think she needs a more predictable pattern, you can also hit her sword back to her when she throws it to stop her doing the teleport attack
the first pair of walljump boots by the lobby are from before i had the actual location created
but as for being able to go to other places, the first boss wont be skippable since they guard the dodge roll, but you wont be forced to go there as soon as you get the walljump boots (where the villain turns the screens on)