How to fix this water damage to ceiling?

Please see the picture, what's the best strategy to fix this? The skin which is quite thick is peeling off but the back end is quote solid. I have stopped further water leakage.

Should I be cutting the dry wall piece and put another one or I can manage fixing it without that?

Should I rip of the nearest crown molding as well and put it back?

Or this project better left to a professional?