I don't think it's possible because at shutdown the system is trying to do just that, i.e. shutdown. So, at shutdown, you need a tool (or script/batch file) that gives the command to: 1. Start the backup & 2. Shut down the system soon after it completes.
Anyway, try the solution at click here. First create the script file, then scroll down to option 4 where the use of the free Xecutor comes into play. Provided download link doesn't work, so get it from click here / website for more info click here. G