The city bells tolled ominously; warning of the turmoil unleashed within the castle walls.
^ Replace the semicolon with a comma. Semicolons are only used between closely related independent clauses which are not joined by a coordinating conjunction.
- Run-on sentences - There are quite a lot of run-ons like this one:
Slowing his pace, he deliberately displayed signs of exhaustion, allowing the pursuing guards to gain ground, closing in on them.
You can just separate them into independent clauses or you can use em dashes to mark off extra information that is not essential to understand the sentence. The purpose of this is for ease of reading.
In one motion, he spun around and smashed his gauntleted fist into the head of the first approaching guard, instantly crumpling him to the ground.
"Crumpling" is not the proper word to use here. A human cannot be crumpled. That sounds so weird. Consider revising or using "knocking him to the ground" or "collapsing" instead.
If he shouted, then you should use an exclamation mark.
“Come on,” he bellowed, assuming the lead as they spurred their horses into a gallop.
Same issue here. Bellow is a loud roar so there should be an exclamation mark rather than a comma. Also, "assuming" is not the right word to use here. Consider revising or using "taking the lead" instead.
He blocked the last guard’s sword and moved in close, striking his chin with his elbow, before rapidly turning around to stab his sword through the man’s ribs.
I've read plenty of suggestions when it comes to writing fight scenes and the most common advice is: to use shorter sentences.
Have a look at this article. It's really helpful.
https://nybookeditors.com/2018/08/how-to-write-a-convincing-fight-scene/
New footsteps approached with urgency, and he turned to see her atop one horse, having readied them for escape. He ran to the other horse and mounted. “Where do we go?” she pleaded, her voice shrill.
I also noticed that you tend to put the dialogues in the same paragraph that's not related to the one who's speaking. Like the one above—“Where do we go?” she pleaded, her voice shrill—should be on the next paragraph line.
“Hello, Princess,” the man said as if greeting an old friend. “I must admit, I was expecting your highness some hours ago.” His words startled her; he spoke without even looking at her. “I suppose it’s to be expected. It’s not every day you would visit the dungeons,” he said patronizingly.
Or, like this one, why are the dialogues all bundled up in one paragraph? It's either you just go like this: "Dialogue here blah blah," he said. "Dialogue again blah blah." OR separate them into different paragraph lines.
“To the gates,” he said with steel in his voice.
"Steel in his voice" is so weird. I get what you're conveying but it still sounded like an actual steel is embedded in his voice—doesn't make sense right? Consider revising or using "he said firmly" instead.
The knives flew true, and the guards fell to the ground, opening a narrow path for their escape.
The sentence "The knives flew true" doesn't fit well. Consider revising or using "The knives hit their targets" instead.
+I spotted a few more words that aren't the best to use or are entirely not proper to use in the sentence or action. Please consider proofreading.
Why had her father commanded her to speak with this prisoner? Lost in her thoughts, she hesitated, unsure of her purpose here.
If it's a thought, you should
italicize it or use ' '.
“I must admit, I was expecting your highness some hours ago.”
Capitalize Y and H in Your Highness.
It had been only two days since this man had stormed into their home, freed the bride-to-be, wreaked havoc among the guards, and endured torture. Yet there he sat, unnervingly calm. It unsettled her deeply.
"Yet there he sat, unnervingly calm." isn't a thought, or at least doesn't seem to be, why is it italicized?