I'm trying to make my FMC a gun-toting badass with intimacy issues but even though I have her shooting off her mouth as much as her gun she still comes off as weak.
I wonder how often your FMC shoots off her mouth, and under what circumstances she does so.
Personally, I don't feel "shoot off her mouth" necessarily means strength. It could give me an impression of an overly-emotional loose cannon instead.
Can a woman be seen as strong in a story and still cry, have panic attacks, and run away. What would make her look weak? How could you make her look strong?
This all depends on your definition of strength.
Does strength mean you never run away? Does this mean that even if you're caught in a war zone and your only hope of survival is to flee from an oncoming army, like what happens to Scarlett in
Gone with the Wind, you're weak if you do so? Scarlett has many faults, but weakness is not one of them.
Oh, and on the subject of
Gone with the Wind, Melanie is never the sort of woman who yells and blusters and refuses to take any shit from anyone. She's quiet, shy, polite, and self-effacing. But she is incredibly strong. Her first line of spoken dialogue in the book is courteous disagreement with her fiance, showing that she knows her own mind and does not let other people, even the man she will marry, sway her. And she will do anything to protect the people she loves.
Also, why would strength mean you don't cry? This equates tears with weakness. I think it's healthier to cry, under certain circumstances, than to bottle everything up and pretend that you're unaffected by it. As frimble said, a character who cries and runs away all the time would be annoying, but tears alone don't mean weakness to me.
By the way, this is one of my favorite quotes from
A Game of Thrones on the subject of strength :
Bran thought about it. "Can a man still be brave if he's afraid?"
"That is the only time a man can be brave," his father told him.