When I slapped a lady on the backside she asked me to apologize, but I don't want to.
Wait, hold up. How did this all start?
She has mental problems and has now come after me aggressively
If you hit someone you could be charged with assault. You should apologize and pray they don't hit you back or call the cops.
What? Why would I do that?
You hit them first and now you're saying that they're insane and aggressive. It seems to me like you may be the one in the wrong here, and you shouldn't ever strike someone that you don't know.