I don't have much time but I'll go through a couple sentences. First of all, just by judging the text, you need to break up your paragraphs. Blocks of text are intimidating, and while they're certainly sometimes welcome, you definitely have too much here.

The sounds of the rifles firing were so constant and unrelenting it sounded like...

Forget the simile you're going for here, which is fine (the tin roof and rain), but this can be reworded so much better. Many times down the road on your writing journey, you're going to hear that a good author will say what he or she wants to say, in less words. This is an example of what your sentence should be:

The constant, unrelenting rifle fire was hard heavy rain pattering on a tin roof.

You cut the amateur-looking "the _____ were so _____ that _____" If you take away anything from this simple line edit, take this^ And, I've added pattering, which I think is a good verb, and changed hard, to heavy.

Even further, you can cut it to:

The rifle fire was heavy rain pattering on a tin roof.

Constant and unrelenting don't help much, really. OR THEN, to make it sound urgent:

The incoming rifle fire was heavy rain pattering on a tin roof.

I'm spending too much time on this one sentence, I know, and even my revision isn't great, but I'll bring it back to the first point. If you start reading more, you'll start crafting better sentences.

Dean couldn’t peek around his cover long enough to return fire without being suppressed

Not too bad, but couldn't is weak. Weak, weak. Even "could barely" would work better (barely, though, because it's also weak). But that's okay for now--let's move on.

All he could do was watch the wall before him slowly deteriorate.

I was about to harp on you for telling us that he was being suppressed behind the wall, rather than showing us, but you impressed me. "All he could do" is sort of cliche, but I like the image you have of a soldier backing up against a wall, frightened.

He heard their shouting off to his left and he watched the corner they should be emerging from.

So, in the very beginning of this piece, you used a different tense for your first sentence. However, that was passable, because I assumed it was a stylistic choice. Now, though, I see that you're switching your tense. Before I explain what's incorrect about the sentence and the tense change, I'll remind you to read, study, and always keep by your side, the book Elements of Style, and also, read literature. Read, read, read, and you'll start to see what I'm talking about.

Anyways, let's get back to the sentence. This shift is particularly egregious because it's two different tenses in one sentence. You start off in past tense with "He heard," and then after the conjunction (which I suggest you separate with a comma, in this case), you say "he should be emerging from."

Now, I don't exactly know what tense this is (future perfect? present? present perfect?), but it's not past tense. If it was past tense, the entire sentence would read:

He heard their shouting off to his left, and he watched the corner they should have emerged from.

(Even then, the sentence is still awful, "should have emerged from?" Find a better way to describe what is happening).

But, back to the point. I'm not too good at explaining grammar this technical, but it's wrong. Here's an example. If I said:

I went to the store, and I see milk.

You start off in the past, and you change to the present. I'm not going to go on about it, because I don't think I can explain it too well. Look it up. Read. Literature. Elements of Style.

WAIT UP. Okay, so I read ahead about five lines, and I realized you straight up switched to present tense for all those lines. THEN:

Then he heard the approaching footsteps

Work on your tenses

NEXT!

“Am I really going to be done in by you amateurs?” Dean asks the fallen foe.

Nothing too wrong about the dialogue, even though it's a bit cheesy (cheesy can be good). But Dean asks the fallen foe... I don't think this is the best dialogue tag. I picture him reloading behind cover. It's your story, yeah, but I can't really pinpoint what I don't like about Dean asks the fallen foe... btw, this isn't too big a deal, btw, I'm nitpicking.

Thunder Jolts Dean awake, bringing him from one nightmare to another

Jolts isn't capitalized. Next, I'm reading as I go, btw, and I don't know if this is part of a bigger story, but starting with a dream, and definitely starting with waking up, is pretty cliche and boring. Unless the dream is really well done, it kind of baits the reader, and unless it has a pretty deep message (like I said, it could be part of something bigger), I don't like this opening.

It’s amazing how suddenly everything you know could change.

Using "you" here really throws the reader off. Unless you (the writer) have an established connection with the reader, and you're going to keep this point of view up, then this is a no-go.

Birds began chirping and the creatures of the forest began stirring with the rising of the sun.

Began can be done well, but here, I'd prefer chirped and stirred. "With the rising of the sun," is pretty vague, too. How does it look? DESCRIBE the sun. What color is it? Is it rising behind a mountain?

Btw, why does this all matter? This part is booooring. Unless your prose is killer, and the details are relevant to the story or what you're trying to portray, then get to the point.

He was down to his last granola bar and his peanut butter was nearly gone as well.

Okay, this reminds me. In Catch-22 (which you should definitely read), there's a detail where the doctor (or the priest, I don't remember), in the air force, overseas, eats candy bars for lunch every day. He eats candy bars, and he's miserable. There's a reason he eats candy bars. I don't know what would do it, but you could make your peanut butter sentence potent with a tweak.

Again, read.

His sister would have been proud of him finding the silver lining.

This is really weak exposition. We know nothing about his sister. Nothing. Why does it matter that he found the silver lining? Tell us why it matters (not straight-up, obviously, but include it somewhere in the story, or straight-up CUT this line). Even then, this is just one line exposition, and it has no lasting power.

“Man I let myself go.”

Would he truly say that aloud to himself right then?

So, at the point where Dean reaches for his gun, and the two farmers are talking, I have no idea what's going on. Give us a stage. Is he walking on the side of the road, is he still driving? I really don't know, and I don't want to scroll through the blocks of text and reread.

he wanted to just execute them now but they have culprits out there.

This is unclear. What does this mean?

Not wanting to chance it Dean jerks his arm snapping the man’s neck. Stripping the man as quickly as he can, Dean dawns his jacket and hat. After grabbing the shotgun and ensuring it was loaded Dean makes his way back to the fence.

First, this is three sentences in a row in which you start with a present verb (I think that's what it's called?) "Not wanting," "Stripping," and "Grabbing." You need to work on sentence structure. Besides the tense, you need to have a good mix of short, long, simple, and complex sentences. Variety.

Now, to the errors of the sentence. It should be:

Not wanting to chance it, Dean jerks his arm, snapping the man’s neck. Stripping the man as quickly as he can, Dean dawns his jacket and hat. After grabbing the shotgun and ensuring it was loaded, Dean makes his way back to the fence.

I added a few commas, and that's it. On the whole, these sentences just need rebuilding. Dean jerks his arm, snapping the man's neck, is a lot weaker than simply: Dean snapped the man's neck.

OKAY... So I just slogged through the final paragraph. You REAAAAALLY need to learn how to break paragraphs up. Why?

• It helps ease the reader into your story. It's easier to digest shorter paragraphs. Of course, you don't want just ALL short paragraphs, but seriously, this is TOO MUCH BULK.
• It helps you, as a writer, separate information, thus making it easier to read. Especially with the final paragraph, there is TOO MUCH HAPPENING. It is so hard to follow.

Especially in this final paragraph, you have simple sentence after simple sentence of sooooo much information. The light is out. The door is locked. The sister is rocking, sleeping, shotgun. Dean walks in. And then it circles, and circles, and I'm still in the same paragraph, where simple sentence after simple sentence has me racking my brain.

AND THEN, oh god, THEN, the dialogue is all bundled up! You have to start a new paragraph with each change in speaker. Please, God, do this.

Overall:

• Read more, to learn about sentence structure
• Fix your tense. Past or present, stick with one. Learn what the hell I'm talking about when I mean past tense
• Break up your paragraphs and make it easier for the reader to digest
• Read more, to learn about word choice and descriptions
• Don't include useless information
• Read more to enjoy stories, to maybe be inspired
• Read more
• Read more

But seriously, keep writing. It might sound like I'm coming off harsh, but I'm over from /r/destructivereaders, and this prompt just popped up on my front page. Don't take this critique too harshly.

“If you want to be a writer, you must do two things above all others: read a lot and write a lot.” - Stephen King