Luckily you don’t have a very large area to repair so it shouldn’t be very difficult. When repairing any water damaged areas it’s usually a pretty good idea to stay away from your normal spackling compound. Most lightweight or fast dry spackles are water soluble and what it looks like to me is the water from the paint broke it down causing it to shrink. In order to fix it the right way without replacing the section of drywall you will need; medium to fine grit sandpaper, plaster or drywall compound, a putty knife, a paint brush, and some oil/shellac based primer sealer.
First you want to remove all the old water damaged paint if you haven’t already, this is very important because your repair job is only going to hang on as good as whets underneath it. You will just need to lightly scrape and sand the affected areas until you feel you have a good base for your repair and the new paint. Next you will want to dust the surrounding area off removing any loose chips and dust from the previous step and you are ready to prime. It is important you use either a shellac or alkyd(oil) based primer to prevent not only any residual moisture in the drywall from damaging your wall again but to prevent cracking, bubbling, or even stain bleed in the future. Once the primer is dried completely you are ready to patch or skim coat the damaged area. Going with a thicker wallboard compound is important not only that it sands very easily but it will provide a stronger repair. The plastering may take a few coats as it will shrink as it dries. Once it is completely dried you are going to need to sand it smooth, the area you’re working in will make sanding a pretty easy job. I prefer to use a sanding block when I do any skim coating because it helps level everything out at an even rate but it’s not 100% necessary. After you have a nice smooth surface dust off the wall and throw another coat of primer on it, sometimes once it is primed you may notice some small surface imperfections make sure to re-patch and prime them. If the wall looks and feels good at this point finish the job off with a topcoat of paint and you should now have a nice even repair that wont damage nearly as easy as the spackle. Got any more questions about how or why you need to do something let us help you out.