Surface mildew is easy to eradicate with full strength white vinegar. If your bathroom walls are growing mildew, wipe the mildewed spot with a vinegary rag. You could also spray on the vinegar, let it sit for a few minutes, then wipe it dry. If the mildew has left a stain, try spraying hydrogen peroxide on the spot, waiting a few minutes, then rubbing the area dry with a clean cloth. Repeat as needed.
If you have very persistent patches of mildew, try this. Put some white vinegar in a glass jar and add an inch long section of copper wire. Let it sit for a few days, then pour the vinegar into a spray bottle, leaving the copper wire behind. Do not leave the copper in the vinegar longer than a couple of days, or too much copper will dissolve into the vinegar, and you will end up with a solution that will dye your walls a bluish green.
Use the coppery vinegar to clean off the patches of mildew. Copper kills fungi, and the tiny bit of copper that has dissolved into the vinegar will help prevent the mildew from returning. Wipe the walls dry. You do not need to rinse the walls.
If you have mildew patches that have been on the walls for a long time, make a paste of borax and water, and scrub it with an old toothbrush or scrub brush. Leave the paste on the wall for a couple of days, then vacuum it off. If you allow mildew to grow for a very long time, it will penetrate the walls and you will need to replace the wallboard.