First, let's take a look at what makes a good action scene from one of the masters—Jackie Chan. In the video below we see Jackie's rules for action comedy. While this video is meant for film students, many of these lessons apply to writing in a beautiful way.
1. Give the protagonist a disadvantage
This is essential for building empathy in a fight—yes, fights are great spots to develop characters.
Depending on where we are in the story and who's fighting, readers know who is going to win the fight. Jack Reacher isn't going to lose to random bar thugs. So we give the hero a disadvantage to make the fight interesting. Since we're not wondering who is going to win, we give the hero a handicap so severe that we wonder how he wins. For example, our hero is a martial arts master, but how is he going to beat five ninjas when he's tied to an interrogation chair?
As the battle unfolds, the hero works to overcome his disadvantage, making us begin to root for him. Each action is followed with a logical reaction, building to a joke, a finishing blow or—even better—a situation where the hero forces the disadvantage on the enemy.
2. Foreshadow the environment, and use it
This is related to Chekhov's Gun: "If there is a gun on the mantle, it must go off."
This also ties into point number one. The environment can be the source of the hero's disadvantage. For example he could be fighting scuba divers underwater, only he doesn't have an air-tank.
Otherwise, if the protagonist is climbing an endless staircase, holding onto a cold steel railing, then we want to see him and his enemies tumbling down that staircase. And somebody has to break their teeth on the railing.
In film, Jackie makes the action clear by using a well-lit setting. In writing we achieve clarity by cutting unnecessary words, making the important images stand out. This goes back to the Irony of Speed lesson.
4. Show the strong hits twice
"Wait," you say. "Isn't repetitive writing bad?" It is for the most part. And it's especially bad in action. But the question we should be asking is why Jackie shows the hit twice. It's because he wants you to dwell on the hit, to let it sink in so you feel the impact.
So maybe this section should be titled Dwell on the strong hits. In writing we make the reader dwell on something, like an emotion or a revelation, by stopping the flow with a stone-cold period, or a paragraph break, or a scene break for extra impact. It works the same for action. The longer the reader stops to register the blow, the more powerful it is.
It's important that the protagonist gets beat up, made a fool, and hurt. It humanizes him.
The narrator in the video makes a great point about Jackie: He doesn't win because he's a better fighter, he wins because he doesn't give up. That relentlessness shows his character. And that's the kind of hero people cheer for.