You will rip the heck out of the drywall trying to remove it.

Sand down any visible seams, then prime it with a non-water based paint, such as the white alcohol-based stain killing stuff.

Then paint.

Yes, expect to have a huge mess. I had a bathroom with that problem. Since the surface was vinyl, I had to remove it. The mess was terrible. I got the vinyl and the paper backing along with a lot of the drywall paper off the walls. I coated the bare gypsum with Gardz. When it dried, I kept filling the deepest dents with thin layers of joint compound, then eventually did a skim coat of the walls. More Gardz, good primer then two coats of paint. It looked good and held up well. But it was a lot of work.

Having removed layer after layer of painted wallpaper, it's not something I recommend. A lot depends on how picky you are. Painted wallpaper never looks great, but you may decide that it's "good enough" when compared to the work to remove it and patch the walls. If you go that route, you have to remove any lose paper, sand lumpy seams, etc. then seal it with Gardz, then prime and paint. It may still bubble or loosen, but that's your best shot if you want to paint over it.

Despite what "lazy" said, just remove the paper. Most likely it will come off with little damage if done properly. Painted wallpaper is just that and never looks good.

Here is a link that might be useful: stripping

I was in the same situation.

I first rented a steamer and went at it. It worked, but it was very unpleasant and messy.

I then read where fabric softener mixed with water can be used. You have to keep reapplying it, but its a lot better than the steamer and its not like using serious chemicals.

Both options require first using a paper tiger over and over.

No serios chemicals here, it comes for California!

Here is a link that might be useful: safe and simple