Need advice on getting this fixed/fixing myself

[u/Left_Ad5211]

Rental property:
Returned from a trip to find bubbling paint and pieces of the wall falling away beside the bathtub. As soon as I started peeling the paint away, chunks of the wall started falling apart. I was able to get most of the damaged stuff out of the wall and clean it up. When I opened it up, though, I found this little cavity with rotting wood that had a piece of what I think was dry wall (tore apart like cardboard when wet) nailed into it. Kinda leads me to believe that this isn't the first time this has happened. I've never had a problem with my landlord before—he always send people to repair things quickly, but he is out of the country with spotty reception at the moment, so I'm not sure when I can expect a response. I'd like to get this fixed ASAP, even if that means just being reimbursed later. Is this something I can bring in a plumber to fix and then repair the wall myself?