It's kind of been touched on before, but I think having it said more clearly would help: Your character's history should inform their fighting style and skill. Would they have had an interest in martial arts? Opportunities to learn it? How about purely self defense techniques? Did they go through any harsh times as a kid or young adult that would require street smarts? Do they have weapon training? Are they a trained combatant (military or otherwise)?
You want to know exactly where your characters stand on all these questions so they know how to act. Like it's not really enough to say "they go with the flow", because everyone would have a style and a preference for offense vs. defense, incapacitate vs. kill, fleeing vs. fighting, emotional vs. rational, etc. And every style of fighting has its own strengths and weaknesses.
For example, I'm a black belt in Tae Kwon Do. It's known for being a heavy kick style with strict form and (at least where I was taught) focused on self defense. I'm sure if you googled something like, "difference between martial arts styles" some sort of list will pop up. There is also a large difference between "realistic" technique and "show technique". For example: Even though it's seen a lot in media, punching/kicking/even aiming a gun at the face is generally a bad idea and more ineffective than you would think.
Punching? Your knuckles are actually kind of weak and you'll probably break or injure your hand if you don't know how to punch. Especially something harder like a face.
Kicking? Assuming you are that flexible to kick that high (most adults are not), even if you hit, you are WAY easier thrown off balance with your leg above your center of gravity.
Shooting? The head is a small target. There's recoil, wind, and the target is probably moving. Even a trained combatant is not going to land headshots often.
Generally speaking, no matter WHAT you're doing, you should probably be aiming at the torso. It can take more of a beating, but it's a much bigger target. And if you aim right, you can knock the wind out of them by hitting the solar plexus. Groin shots or joints (in close quarters) are good incapacitors, too.
There are also certain parts of the body that are harder than others and "safer" to use to attack since they're not as easily injured. Palms (the base), elbows, knees, heels, and the ball of your foot (assuming you can curl your toes up enough to not injure them) are the main examples. Elbows and heels were best in my experience. There's a reason that when we had to break wood boards during belt testing that they would not allow you to punch the board unless you were an adult and VERY CONFIDENT in your ability. I had the easiest time breaking a board with my elbow.
I kind of rambled there but I thought it was important to mention some differences from media. Extensive acrobatics are also WAY harder than one might think. And frankly, if your character has never really fought someone before, they're better off trying to escape. They also will likely not be thinking clearly and will either freeze up or freak out. The medical side of it and the seriousness of certain injuries and the recovery time is also something you should really consider.
Of course, fiction is fiction for a reason--half of the fun is making it fantastical. But that's going to depend on the tone of your story and its world. I think even if you have a complete fantasy, grounding SOMETHING in realism still helps keep believability and enriches it. A good example would be Avatar: The Last Airbender. Every group uses different martial arts and weapons and it makes a simple battle of elements way cooler.
As a closer, I also can't emphasize enough how important it is to make the conflict mean something emotionally. If the audience isn't invested in the idea of the fight or both characters, it has a real risk of feeling like filler. A lot of shonen eventually fall into this trap.
And honestly? I personally love comics that show tactics or ways to get around conflict other than violence. Makes it more interesting. So try not to get stuck in a rut of people beating on each other.