my battery is no good and I can't back up my phone. Any ideas how I can backup??

If you suspect that the battery is causing your iPhone to reset that often, it could indicate a faulty battery. I'm assuming that it still does this when you connect this phone to its power adapter ... correct? Also, I'm assuming that you tried "force" restarting the phone and resulted with the same. If all of this is true, you basically only have the option to have the phone looked at either by Apple or an Apple Authorized Service Provider. Attempting a backup, until you do, may prove fruitless. Hopefully, you have been doing them all along before this issue arose.