I'd check battery lead/terminals before condemning the battery (and spending money), I'd certainly remove battery leads, clean and retighten before anything else. But would agree with Richard that most likely culprit is failed/failing battery.
That's low, link below suggests AMG 12v lead acid should have 12.89v when fully charged.I just checked the battery with a voltmeter, after charging, which did not take long it was reading 12.2 volts, that should be OK I thought?