Listen, here's the way to do this. First, buy batteries with the lowest-voltage cells you can get. If you're going to spend $1000 on batteries, get 6-volt golf-cart batteries at least, or perhaps even a battery of 2-volt forklift cells if you can find one cheap. They will last longer, and losing a single cell won't be as catastrophic. Secondly, make sure to get a pure sine wave inverter with a surge rating that's appropriate for starting an air conditioner compressor. It takes a lot of power, but 2000 watts should be plenty as long as the inverter is well-made. Consider a 24 or 48 volt inverter, depending on your battery bank. Lastly, you definitely need more than 300 watt solar cells. Even the smallest air conditioner uses around 600 watts while running. If you want to run the air conditioner more than 3-4 hours a day, you'll need more solar cells. And, lastly, yeah use watts and watt-hours because your calculations are all wrong. Learn to use
Google Calc. A battery bank that's rated 400 Ah at 12 V can store 4800 Wh of energy, and will run an 800 W air conditioner for 6 hours.