swag....
Googling, I see that a 13000btu RV AC draws about 13amps at 120v. If your 12v battery is providing this through an inverter, it will be drawing roughly 130amps from the battery. There are also inefficiencies running through your inverter that will probably result in 5-10% more amps needed. So my swag/guesstimate is that your AC will be drawing ~140amps from your battery. Assuming your battery can handle this and that all wiring is adequately sized to reduce voltage drop/etc, it looks like your battery will power your AC for about 1hr 20 minutes. This assumes that your battery was fully charged and you aren't drawing significant power running anything else.
Summary: Not long at all. Use a generator to run your AC
Good luck!
Chris