Mods, if this isn't the best location please relocate or if this is something generally not acceptable here please nuke and let me know (and please accept my apologies in advance!).

I am doing some work in my bathroom that has a skylight. I noticed the paint peeling up close to the skylight. I can scrape/sand/paint the wood frame of the skylight no problem. However, the paint is bubbling and peeling in some spots of the drywall and I can scrape some of it off but in general it's not coming off easily. See photo (discoloration is from scraping with a taping knife). I am looking for advice on what to do here without doing a ton of work. Not on the table: replacing the sheetrock. I am looking for a 5 year repair here as I don't plan on staying in hawaii any longer than I have to. Any thoughts would be greatly appreciated. Thanks!

I don’t see the photo.

My guess is the bubbling and is caused by water coming in somewhere by the skylight.

You need to address stopping the leak first otherwise the bubbling will return.

After the leak is addressed, I think the bubbling may shrink enough that you don’t notice it.   Otherwise scrape/cut it off and use “orange peel” drywall repair spray

Move to Off Topic section.

Fix the leak first

Need to see a photo to advise.
Before scraping would have been nice but whatever you got should be good.

First, if it's just the paint bubbling, you can sand and scrape that off, then smooth it out with some drywall compound -- feathered and sanded, then paint.

If the drywall is damaged (wet, crumbling, paper bubbling), then you should consider replacing the spots that need it.  Surface repairs on damaged drywall won't last.

As mentioned, if there's a leak, address that immediately,  If it's just moisture from bathing and showering, then the drywall ought to be serviceable. 

Any spots that you sand or scrape that result in the drywall paper being damaged or removed, use drywall compound to cover it, just like you do when "mudding" drywall joints. You can use drywall tape if necessary to cover large areas. Tape can strength the drywall so it's less likely to crack or chip, but for small areas, just compound should work.

Don't use the compound that comes in ready-to-use buckets/containers.  Buy the powder you mix with water.  That way you can control the thickness for better ceiling applications.  You can buy in larger bags for big drywall jobs, or smaller boxes for repair jobs.

The Easy Sand brand is a good choice.  Get one that has the working time you need -- i.e. how long can you work with it after mixing before it's too dry/hard to properly spread).  The Easy Sand usually has a large number on the front of the box or bag that corresponds with its working time in minutes.  45 is a good one to get.  It dries in a day for sanding and painting while giving plenty of time to apply it.

Mix it dry enough so the compound isn't going to fall off the ceiling, but wet enough to work it to a smooth-ish, flat surface.  Once dry, add a wider layer if needed to feather it out and hide any high points.  Let it completely dry, then sand and paint.

Plenty of YT videos on doing drywall.  Look for specific info on the powder compounds and how to mix.  Very easy to use.