The most common cause of those areas getting wet are the result of water being splashed onto the walls, but it can also be the result of water leaking THROUGH the walls, either at penetrations through the tiling (such as where the tub spout and faucet handles are) or through leaking grout joints.
I've never heard of XP or Barney board, but you can use any panel suitable for use in wet areas there, like the Durock previously mentioned or Dens-Shield. I wouldn't use greenboard because it's not as water resistant as you need.
A very common cause of the problem you're experiencing is water penetration through the tiling. You see, enameled steel bathtubs have a "lip" around them which is about an inch high. If water is leaking through the tiling, then the water will drip down the back side of the wall and be carried to either the front outside corner of the tub or the back outside corner of the tub, where it will drip down the side walls and get them wet, just as you're experiencing.
If you suspect water is splashing onto the outside of the wall, the best splash guards I know of are called "Splash Enders". Or, at least, they're the only ones I know of that are actually made of a plastic that silicone caulk sticks well to. The other ones tell you to caulk them in place, but silicone doesn't stick to the kind of plastic they're made of, so they're continuously falling out of place.
If the Splash Enders don't solve the problem, then check to see if water is penetrating through the wall at the faucet and tub spout openings. If those look like they're properly sealed up, then your best bet would probably be to put up a tub surround over your ceramic tiling until you can get that tub/shower redone. It's often very hard to find leaks in ceramic tiling simply because the grout may not have stuck to the side of some tiles, and when the shower water sprays on that part of the wall, water can seep through the tiny gap between the grout and the tile edges.
It's way more work to try and regrout ceramic tiling than it is to replace the tiling.