"Strong" female characters in movies, books, etc.

To me, it seems like movies have four types of roles for women:
1. The damsel in distress. (E.G. Most Disney princesses...)
2. The "hot" girl that wears skimpy outfits who thinks she's better than everyone else and only cares about hair, makeup, and boys. (E.G. The "mean girls" in those romantic chick flicks about teenagers in high school.)
3. The woman who has all these superpowers, but always struts around in sexy outfits. (E.G. Women in a lot of sci-fi and fantasy movies.)
4. The tough tomboy who has that "don't mess with me" attitude who plays sports and/or fights. (E.G. The supporting female role in a lot of animated adventures, and the villianesses in a lot of movies)

Okay, so many feminists have complained about the first three and how aggravating those types of characters are, but... wait! The fourth type of female character isn't annoying! In fact, it's great! Pink dresses and makeup are sexist! Girls should fight and play sports and not do traditional "feminine" things! Being emotional and feminine is the worst thing anyone can do, even worse than murder!! (EXTREME SARCASM)

Okay, so some girls are like that fourth type of female character I listed. Some girls do completely fit that stereotype. Guess what? That's fine! If that's who you are, great! But these characters tend to be REALLY cliched and uninteresting. Yeah, sure, they sword-fight, and that's pretty awesome, but they tend to lack certain qualities, GOOD qualities, such as sensitivity and emotion, and tend to act very much like how people think men should act. It seems like the filmmakers just sit there and say "hmm, how unfeminine can we make this character." It sends the message that being emotional or sensitive is a bad thing, and that it's the worst thing you can be, which is just as degrading as always making girl characters weak and stupid. Too often in movies the message is sent that "you need to act the way men are 'supposed' to act to be strong," which just isn't true. Besides, characters that lack emotion are so uninteresting. Can't they at least have some emotion? Can't they at least have some sort of personal problem that they have to overcome? Can't they have a deeper background story? These are the type of things that make characters interesting. JUST BECAUSE A FEMALE CHARACTER SWORD-FIGHTS DOES NOT AUTOMATICALLY MAKE HER AWESOME OR STRONG!!! Filmmakers, why don't you make more female characters who don't completely fall under any of the categories listed above? A character that's strong AND sensitive. Someone who deals with hardships more emotional than "a dragon's trying to kill me." A character in between "girly" and "tomboy-ish" (though she may lean on one side more than the other). Thank you.