Car wouldn't start, replaced battery; running but now bogs down/stalls when air-co runs

Car has high miles, and is old. Replaced transmission 3 years ago. Had some strange electrical issues (headlights going out for no apparent reason); lights pulsing. For no apparent reason (comes and goes, seems to be seasonal?) Neither problem solved, but neither returned either (although we did have to replace the headlight harness cable that connects headlight to car; it was corroded).
Newest problem resulted today after running this morning and this afternoon out and about returning home no problems, but when tried to start after dinner to run a quick errand it was dead, no clicking, or turnover, lights were dim and radio and dash/interior lights were going on and off.
We assumed dead battery and replaced; great it turned over. However at idle is now having problems when the air conditioner is running. Runs okay with air-co off, but that isn't gonna fly real soon with summer coming. Any thoughts? Cleaned and Tested battery connections; tested Alternator all seem to be good. Going to replace air filter. It is dirty. No codes are being thrown, so I'm at a loss and not looking forward to expensive mechanic bill to find mystery problem. Chevy you make me wanna cry :( although 220,000 miles isn't something to shake a fist at. Thank you, P