What is the best way to redo a shower base?
Unfortunately, yes. The problem is the liner or waterproofing membrane.



The subfloor that needs to be reinforced is below the membrane. The membrane must be continuous up the wall, so wall tiles need to come down. It's possible only the bottom row or two of tiles would have to come down, but that depends on the method of waterproofing used, and if you're okay with the aesthetic (eg: tiles at the bottom looking different). 

If there's no waterproofing layer (possible, since this was installed incorrectly to begin with), then the new contractor will want to install that as well, or their install will eventually have problems (mold, leaks, and/or rotting wood and thus more cracked tiles).