So, about the one thing I clearly understood is you are portraying the female character as rather violence loving, but it seemed kinda one-dimensional. She also comes off as very dumb, like an 80 IQ. In my opinion, dumb and violence-loving are not a very effective combination for characterization. You really should at least make her have a normal 100 IQ level of intelligence. Or, maybe you could keep the 80 IQ intelligence and make her a hard-core druggie. Drugged-up is about the only culturally acceptable way to make a female character both dumb and also violent.
If you go the druggie route, then that helps with the characterization quite a bit. You would make her a LOT more eager on the trigger and have weird side-ways sounding logic that she "NEEDS" this job (in order to get her next fix,) and thus she's really eager to get it done and that explains why the guy is constantly having to hold her back.
If you go the route of making her have at least a normal level of intelligence, you should probably make her pissed off to go with her trigger happiness. She should be a lot more confrontational and get into a bit of an argument for the guy telling her to cool it down. An excellent example of this kind of character would be Levy/Revy from
Black Lagoon Levy is a freaking bad-ass with guns, and a fantastic character study to look into as to why someone might turn out like this.
You don't actually get any history into Levy's past the entirety of the series, you don't get some sob story of exactly how she became such an F-ed up sociopath, but you get so much characterization absolutely dripping from her that you can infer a LOT off of her.
Actually, as a matter of fact, I would STRONGLY recommend watching Black Lagoon in order to get some idea for your characterization in this story. It tells the exact same kind of story, a crime drama sorta thing, except that it's VERY ultra violent to an extreme. However, the characterization in this thing is everything.
Another resource I would not recommend as highly but could still help you is
Detective Conan which is very much a detective series in something of a pseudo-noar style in that it makes noar homages everywhere. The primary villains of the series, Jin and Vodka, very much fit the dynamic you seemed to be going with these first two characters, and while being the flattest of the Black Organization characters (Black Organization being Conan's name for the primary villains' organization of the series, since he has never learned the actual name of the organization) they still manage to come across as very imposing and intimidating, and do still have some good level of characterization to them. The only problem, and the reason why I place Detective Conan low as a recommendation, is because there is a LOT of filler and the episodes where the Black Organization is involved are very few and far between, at a rate of about 1 plot episode for every 20 episodes dedicated to a 50/50 mix of filler and B plots. (and there are a lot of B plots.)