I think you may have missed the point with Black Widow (and to be fair, the movies do this too). She’s not a fighter, she’s a stone cold killer. It’s a small, but significant difference. Basically, she’s the member of the Avengers Fury keeps around in case he has to order the execution of the other Avengers. As a Marvel hero, she fits into the same family as the Punisher. The difference is: she’s more efficient. At this point, she’s one of the Marvel universe’s equivalent to James Bond.
The acrobatics style with Black Widow only works well in the movies and the comics (though they’ve moved away from her bouncing around in the last ten years or so) because it’s visually interesting. In a written format, you don’t have that advantage. Gymnastic based martial arts involve a lot of complex physical movement which makes them hard to convey clearly on the page. They’re also very physically taxing, inefficient, and difficult to sustain even for well-conditioned warriors.
Instead, a form like Systema (also Russian) that focuses on brutal efficiency and finishing the enemy quickly is best for someone like Natasha. It also emphasizes her personality traits. Stark, uncompromising, ruthless, but starts with an unassuming posture that lulls the target into a false sense of not about to die horrifically. This is the other thing to remember about Natasha, she’s an ambush predator and she lives up to her codename. Sex is just another weapon in her arsenal and one she’s not ashamed to wield (and if you want to write a character like this, you can’t be ashamed to let her). That said, she doesn’t make for a good faceman. I know I said James Bond, but she’s an assassin not a spy. If you want a spy, get Fury or Maria Hill. It’s all there in her codename: Black Widow.
To really do this well, you’re going to need to do two things.
First pick up a guide to Military Hand to Hand, I just found the SAS and Elite Forces Guide Self-Defense: Self-Defense Skills From The Word’s Most Elite Military Units by Martin J. Dougherty. It’s geared towards Self-Defense, but it has a lot of tips and strategies that will help you write a character geared toward practical and efficient combat. It also comes with helpful diagrams that will better help you visualize as you write. Simple, straightforward techniques are best. You don’t need flashy movements to convince me your character knows what they’re doing, you need to communicate the right outlook. Your character has to sound like they know what they’re talking about as opposed to looking like it. (If you’re really serious about Black Widow, then the character is also going to need to be skilled in other variants of weaponry like handguns, rifles, knives, seduction, and a wide variety of practical job related skills).
The second thing you need to do is sit down and ask: who do I want this character to be? Are they a fighter or a killer? Black Widow is a killer, she kills some people to save others. She kills for the greater good. Sometimes, she kills because of personal reasons or because Fury convinced her to. You need to firmly establish this in your mind because it’s a key part to the MU Widow’s outlook and personality. She’s business first and goal oriented. She makes Matt Murdock the girl in their on and off again relationship. When she’s written right, she’s exceedingly Russian. She also tends to kill first and ask questions later, unless she’s given a reason not to. She’s intelligent, a tactician, and she’s great at advance planning. She’s also cunning, underhanded, great at lying, and not afraid to strike first. She has a code of honor, but it’s not the same one as the rest of the heroes she runs with. She’s not noble in the traditional martial artist sense. She’s a realist. Dirty jobs have to get done, often in the dark where no one can see. This is her role in S.H.I.E.L.D. and, most of the time, when she save the world no one will hear about it. She can take out the heaviest hitters in the Marvel Universe by planning ahead and I will never ever forgive Joss Whedon for not having her be the one to take out the Hulk when he went crazy on the Helicarrier.
Compare her to DCU’s Lady Shiva. Shiva is a fighter. She kills, but it’s a side effect of her fighting and it’s always in hand to hand because that’s who she is. She’s proud of her skills and constantly looking to better herself, to find more challenging fights, to risk it all. She ascribes to a more traditional martial arts mindset and she has a strong (if twisted) concept of honor. She became the best in the world by fighting her way to the top in one on one bouts. If you asked me who the best fighter in Comics is, I’d say Shiva. Her personality gears her towards that. Black Widow would kill Shiva, but not in hand to hand. She’d do it with a sniper rife from a rooftop and leave nothing to chance. She’s not a knock down, drag out brawler. She’ll do it if she has to, but it’s not going to be her first choice.
They both terrify the ever living shit out of the people they go after, but the approach is very different. You’ll see Shiva saunter towards you and issue the challenge, you won’t see Black Widow for what she is until it’s too late.
The final thing to consider is the question of fame and the impact of reputation. A fighter whose ability to fight is based on ambushes and stealth will be hurt by someone recognizing them on the street or even just among the select groups they work with. You’re going to have to consider what “the best in the world” really means, how it affects their lives, and their ability to do their job. If fighting one on one duels like Shiva is their job then it’s not a problem, if it’s international espionage then it gets a little tougher. (Black Widow is more notorious than famous and she usually makes it work for her, but it still hinders her ability to go unnoticed when it matters most.)
Who you base your character on will affect how you write them, their motivations, and the plots surrounding them. For example, if you were writing a novel that was the equivalent of a Kung Fu action movie then Shiva would be your girl. If you were doing a spy novel or thriller, then you’ll find Black Widow waiting for you in a red Ferrari. You can mix these characters into different genres and break up their parts to make new characters, but each will always contain some facet of the original inspiration and it’s important not to forget.