How can I waterproof a shower wall after a repair?
In my experience, this depends on the installation.  My experience is not huge.

Ideally, what you have is a well-waterproofed shower that otherwise doesn't have problems.  If that's the case, then you should be able to do this.  Take out the tile in an area bigger than where your problem is.  If you have a Schluter-type system behind the tile, then you can open the wall, fix the problem, and use Kerdiband to seal up your seams.  Keep in mind that you're going to have additional thinset thickness as a result, so you'll have to compensate while laying the tile back in place.  If you have some other waterproofing membrane, then probably something like Redgard is something you should get to restore the membrane.  If you actually do not have a membrane, but instead just have cementitious backer units (CBUs) behind tile or, worse, mold-guard , then be aware that your existing system isn't actually waterproof to begin with, but is instead moisture-accepting.  In any of these cases, though, the main thing is to take off way more tile than you think necessary so that you can not only reach the leaking pipe, but make a flat-enough wall of the same material and installation style, then lay the repair tile over the top.

Whatever you do, don't rush the effort.  Time for materials to cure is really super important, so don't ignore the barrier manufacturer's instructions.