For sure you want to protect your privacy as much as you can when you are looking into anonymous banking.
What you want is to find a good VPN / VPS provider with a Windows box located somewhere in an offshore jurisdiction. When you connect to this box you will want to have Proxies installed on your home computer so your connection and IP is hidden public.
Once done, you need fake documents which can easily be bought on the Internet, you want to find someone that is actually able to provide such documents notarized. Once done, find a bank and submit to them and︀ only access the account from the way described above.