After clicking endlessly and waiting for a response from Neopet's servers, I worked on a BD autofighter. It is in the form of a simple greasemonkey script.
Before you run it, you need to edit the script and change the part where it says "equipment = [1, 1, 1, 0]" to your appropriate information. These numbers represent the column and row of the two items you would like to equip. They start at 0, so the leftmost column is 0 and the rightmost is 3. The only applicable values for the rows are 0 and 1 (top and bottom, respectively). To start it, begin a battle with a challenger. I have not tested it in 2P.
Sometimes it breaks because there was "an error sending/receiving data". If you see this, just refresh the page. You will usually have to complete the battle yourself.
It is very buggy. I don't know the freeze rate. It does not handle dying. It does not heal. It is a barebones script, but it is still a lot easier than doing it manually.
PS: If you think it is a stealer script, check the source.