Kristin Cashore's Graceling is a novel with a bad-ass female protagonist done right.
Katsa has been Graced with the power to kill. Her instincts are sharp, her strength and speed unbeatable, and she responds to threats without thought or hesitation. The king uses Katsa as a hired thug, and Katsa, full of loathing for herself and her Grace, believes she isn't worth anything more. To counteract the king's cruelty, she starts a movement of citizens dedicated to providing help to those who need it. When she begins to investigate the abduction of a member of a foreign royal family, she becomes caught up in an unravelling scheme that challenges her ability to survive.
Graceling ticks all the boxes that many stories of literal "strong female characters" seem to miss.
Believable reason why Katsa is able to destroy all comers in battle? Check.
Protagonist must deal with negative reactions to her strength? Check.
Friendship with other female characters? Check.
No underlying message that "fighting = good, femininity = bad"? Check.
Protagonist who says she doesn't believe in marriage, falls in love, and still doesn't want to get married? Check.
Quality writing, wonderful characters and a plot that is difficult to put down? Check, check, check.
Katsa is a wonderfully drawn character: physically strong but confused about her identity, stubborn, kind-hearted, intelligent and brave. She is certainly no damsel in distress, but she has her flaws and insecurities, and Graceling is the story of her coming to accept and believe in herself. To fight for herself and her own rights, instead of just the rights of others. Despite her powers, she is deeply human, and deeply compelling.
If you're looking for an action-packed fantasy novel that still manages to be character-driven and emotion-filled, Graceling is an excellent pick.