This is a tough thing to do for most writers. There is so much going on all at once. The writer often feels as battered as the character fighting the battle. How do you manage to get it all in? How do you describe it all?
I am going to give my beliefs on how to do it. Will everyone agree with me? Of course not, but one of the parts of my writing that at times gets the most praise is my battles, so I suspect I may do something right at least part of the time.
I start with something I try to keep firmly in mind in all my writing. Do NOT violate point-of-view. Ever.
In a battle, this means several things. Most of all, it means that your protagonist can't see everything that is going on. They will see what is going on around them, but they are unlikely to know what is going on across the battlefield. The protagonist may not even know if the battle is won or lost.
Also, always keep in mind that battles involve the sensory, not only seeing, but hearing, tasting, feeling. Probably, not a lot of thinking though. When someone is trying to stick sharp implements in your guts or pierce them with bullets, the chances of philosophizing are slim.
However, think about times when you have been under extreme stress. I have never been in a medieval battle, but I have been in car accidents and had loved ones suddenly die. I have been around people who had these kinds of experiences, so I have a good idea how people react in emergencies and under stress.
Strange things happen to you. Time can do strange things, seem to collapse, hours seeming like minutes and seconds seeming like hours.
You may be so focused on the immediate, that you only see what is right in front of you. Or you may by divorcing yourself emotionally from the stress, even deny that the situation is stressful. Or you may appear very calm although piss runs down your leg. Some may freeze, unable to move. The same person may react in different ways at different times.
While occasionally someone may be very conscious of how they are moving their hands and feet, for the most part this isn't what one thinks about under any circumstances. One is much more likely to think of the whole. Think of physical activities we do under more ordinary circumstances, such as dancing, playing golf or playing tennis. Unless we are taking lessons, most of the coordination of our body is automatic. If we spend much time telling the reader that the protagonist's hand went here while their foot went here, it soon begins to be not only boring but also very artificial and (worse) an authorial intrusion.I'll include a battle scene that is in Chapter Two of Freedom's Sword. I wonder if you think I followed my own rules? Did they work? I'd love to discuss it in comments.
Here newly knighted Sir Andrew de Moray is in his first battle. Part of the Scottish army, they are charging an apparently fleeing English host:
The trap snapped shut.
Cursing, his father jerked his horse into a rearing turn. "To me! To me!"
The English were upon them from both sides. They were in a chaos of crashing lances, of horns, of trumpeting horses. Everywhere steel screamed on steel.
Andrew raised his shield and caught a sword slash on it. His father rammed his lance into a knight's shield. The lance shattered. The knight crashed onto his back under plunging hooves. Lord Avoch tossed aside the butt and scraped his sword free. A knight in a red tabard bore down, lance level towards his father's chest. Andrew threw himself forward, shield high. The lance skirled, screaming, along his shield. Ducking low, Andrew swung, shearing through mail, muscle, and gut. The man was dead as he slumped, bouncing from the saddle as his steed plunged forward.
Andrew's world shrank to his father's back and his sword. An unhorsed knight thrust at his chest. His sword lashed out, knocking the axe aside. The knight darted aside for another try. Andrew rode over him, bursting his head open. One of their men rode by, slumped over his horse's neck.
A lance had gone through his belly and stuck out his back.
Sir Waltir de Berkely, unhorsed, slashed at an English knight but the mount reared. Sir Waltir ducked under slashing hooves. His father slammed his sword into a foe's side as another rode at him, swinging. The blade flashed. His father toppled. Andrew jerked his horse into a rear and shattered the man's chest with a kick. His horse made a small leap over Brian's body, blood trickling from his mouth and head in a crimson pool. He jumped from the saddle. All around rang sword upon sword and men wailed, screaming in pain.
His father rolled over. Alive. Andrew straddled him, shield up. Caught a blow. Swung hard at a mailed arm. Blood gushed over his hand.
A sickening crunch and pain exploded in his back. His vision shattered into broken shards. He was falling. He couldn't yell... Couldn't move... His father's body lay under him on the ground. A jolt jerked his head.
"England!" a voice cried out. "For England and King Edward!"
Andrew drifted into a wave of gray mist.