Use increasingly caustic acid, starting at something like vinegar. If that doesn't work, use oxalic acid, also known as wood bleach. Read up on it before you start using it. It can harm your health without any symptoms, and the toxin builds in your body over your lifetime. But used properly, it can be safe.

I'm not sure if it's proper to use the words "caustic" and "acid" together because the first word is often associated with alkalines. I'm not a chemist. Don't use alkalines on your chrome. I don't know if it would cause harm to your metal, but it won't help with rust. It is generally more dangerous than acid.