Most of the floor of a bathroom should not see any great water leaks or standing water. The average puddle you make getting out of the shower before you can towel off will not pose any great threat. If your plumbing work is up to code, that shouldn't be a concern either. However, a plumbing emergency can pose a greater threat.
For laminate floors, it is generally a good idea to lay down a layer of moisture barrier, like Tyvek, between the sub-floor and laminate, and if the sub-floor is over concrete (doesn't seem to be the case here) another layer between the concrete and the subfloor. This prevents the transfer of liquid water between the layers of the floor, while still allowing the layers to adjust to changes in humidity without forming condensation. For the majority of the bathroom floor this should provide ample leakage protection if properly installed.
Make sure that the laminate, once installed, is well-sealed; laminate's great for providing a wood-like floor, but if water gets under the waterproof (or water-tolerant) top layer of the laminate and into the particle board underneath, the boards will swell and your floor will be ruined. A poly or acrylic topcoat will seal the cracks between planks and help protect the flooring; your flooring dealer can probably recommend a product that's compatible with your particular brand of laminate.
Where you really need to take care is in the shower area. If you have a tiled shower, behind that tile needs to be a waterproof barrier which will contain water that gets behind the tile grout (not waterproof) and direct it to the drain, instead of letting it contact the drywall or subfloor. It is not a terrible idea to install the same type of membrane everywhere in the bathroom, but it's probably overkill especially since you'll be wanting to prevent water even getting that far.
The main source of water leakage out of a bathroom, which you will likely not be able to prevent, is inside the walls. You probably won't know there's a problem until you hear water dripping onto your ceiling, or see that telltale tea-stain on a ceiling or wall. There is not a whole lot you can do to prevent this once the walls are up; the keys to prevention are in proper installation of the pipes in the first place. Minimizing joints in supply pipes, which can swell and shrink at different rates with temperature, and making sure all joints on all types of plumbing are well-sealed, are key to minimizing leaks. Any plumber worth his salt will use the appropriate joining materials liberally (solder and flux for copper pipe, glue for PVC/HDPE, rings and cement for PEX).
At the very least you need to remove the two broken tiles and clean up the edges of the hole so that they are square.
Then, assuming that you don't want to remove any more of the existing wall your best bet would be to stick some batten to the edges of the hole from the back and then you can fix a new piece of waterproof platerboard to that. Seal the gaps and replace the tiles:
![enter image description here](https://i.stack.imgur.com/YS0z3.png)
The battens don't have to be very big - they don't have to hold that much weight. The faceplate for the shower controls will help keep the new board in place too.
If you can, take the tiles off first and leave a border of plasterboard so that the join between pieces of board doesn't line up with the edges of the tiles. I know this will be difficult, but it will help ensure that the join is water proof.
Best Answer
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.