My battery gauge is fluctuating , if I run it without a/c it seems OK, but if I turn on a/c it goes down

Chevrolets are known for having a minor fluctuation in the electrical system. this is normal and ok typically. If the fluctuation is more than a "ripple", you may have an issue developing. Your issue may be an alternator going bad, battery loosing a cell (AAA battery tester is a capacitance tester, find someone with a carbon pile tester. the AAA tester does not actually cycle a load on the battery, it tests internal resistance.), A/c compressor going bad drawing too much current. It could also be the gauge going bad. have the operational voltage checked independently (externally)