When the demo was done on our bathroom, most of the shower walls, which had 4X4 ceramic tile, were removed in sections with the tiles and cement board all in one piece. It was not as messy that way. We were doing a complete demo of the room, down to the studs.

How old is your house? You may not have tiles on cement board, you may have mortar and mesh.

Its 30 years old but the area was rural then, and there wasn't much code enforcement. I assume its green board but might be cement board.

30 years old is a mud set job. And a complete and total gut back to the studs, and start over with proper waterproofing. It's not patchable.

Removing a mudset tile job is not only difficult it is physically demanding because it is so heavy. Make sure you look into what will be involved before you get started.

I don't know about your area but in 1987 I saw many a shower built with green board and then redone a few years later with cement board.

I'm also in a rural area that had no code enforcement in the 1980s. My tub surround is 4x4 tiles on green board, which was standard back then. When I remodel, it will gutted to the studs and properly waterproofed.