I'm not saying the character has to be completely feisty (like Tris from Divergent) but they have to show at least a little determination. Even if the book isn't a dystopia or an action, I still can't stand a female protagonist who doesn't stand up for what they believe in... It just annoys me so much! So yes, as you can tell from the title of this point, having feistiness is sort of a necessity for female characters I like... It's something that makes me genuinely love them as a person!
2) A brain (fairly important...)
Again, I'm not saying they have to be super-duper-Hermione-Granger smart, just that they have to have common sense. Often, in action-y books, the female characters act stupidly – why? To use the classic examples of Violet from A Series of Unfortunate Events and (as I previously mentioned) Hermione from Harry Potter, clever female characters are a lot more respectable. I know the two examples I used aren't from action-y books, but you get the drift...
3) An ambition (I'm not entirely sure why)
I guess this doesn't just apply to female protagonists, but I like the character to have an ambition/dream. An example of this is Jo (from Little Women) – she's an aspiring author. It just makes the whole book a bit more interesting if they have, you know, a goal or something. So, I guess that is something I really like in a female protagonist.
I hope you enjoyed this short post, and I bet you're glad it's not another review! By the way, the picture above was just something I drew on paint!