repair drywall in the shower
The best thing you could do is to put ceramic tiles but since that's not what you want let’s try to think of something else. Firstly you must replace damaged drywall. It is extra sensitive when it comes to moisture or water. You can, and should replace it with moisture resistant drywall which is normally used in bathrooms. Then you should apply some waterproofing layer; something cement based (something like Sikalastic-200 W).But thing that is worrying me is do you have horizontal waterproofing layer (waterproofing on your floor? I'm asking this because horizontal and vertical waterproofing layer should be continuous. Than you can pain the bathroom with some exterior (façade) material which is impermeable to water or you can use something like travertine technique which is more expensive but looks really nice and it’s waterproof.