How do you get rid of mildew inside walls?

Mildew is caused by lack of airflow and moisture in the air. You can get rid of it by using bleach, but that won't deal with the underlying cause. You have to change the environment. Open the Windows or get an extractor system if you can. Make sure that the area outside of the window is clean and dry. If the window is low, make sure than there is drainage so that water does not bounce up into the window frame. Replace caulking as needed.

Get a small spray bottle and fill it 2/3 full of water and 1/3 full of bleach. Spray it on the mildew and let it set in. Wipe it off with a wet rag and repeat until it disappears. This method also works on bathroom walls where mildew and mold like to accumulate over and near the shower.