Best way to prep peeling and blistered drywall?

Time for some (more) work. Dry out the room and drywall as much as possible. You will need to sc down the high spots and remove the loose spots, be careful not to poke holes through the drywall and if you do, those will have to be repaired. Once you are done with that, you will need to skim the entire wall with drywall mud, then sand it smooth, apply any texture you wish, prime the wall, then paint it.