Strong female characters require a lot more than mere muscle or a quick trigger finger. Both these attributes can be fine, but they’re precisely that–attributes–not a personality. Left on their own to define any character, all they can do is prop up a cardboard cutout of what was supposed to be a person.
Writers who make this mistake often do so with the very best of intentions. They generally want to write a woman who can handle herself in confrontations and be the story’s hero, subverting the tired old “damsel in distress” trope. And that’s certainly fair enough (I hate that trope, too!), but the key to any strong character–male or female–is a three-dimensional personality.
How about an example?
Agent Dana Scully of The X-Files is one done very right. Yes, she is tough. During the show’s run, she is adept in situations regarding fighting or gunplay. But there’s so much more to the character. She has a soft spot for junkfood (and even longs for a pizza while performing an autopsy!); has complicated relationships with both her partner and her family; possesses an analytical, scientific mind; and examines her faith at various points in the series.
So, what does the above list of traits have to do with Scully being a strong female character? Everything. Because even if she didn’t know how to fight or use a gun, she’d still be a strongly written character. Period.
As mentioned earlier, this doesn’t mean that a strong female character can’t be a badass, merely that she has to be more than that label. Vulnerabilities, quirks, and unique perspectives are part of what makes any character “strong,” and women should never be an exception to the rule.