This is really long, so there is a tldr at the bottom in case you want to skip to how its applied to your genre.
So I think there are basically three main principles for great horror of any type. And I don't think it is specific to natural settings. The first two apply specifically to horror and basically boil down to this: the key to horror is not in what you tell the reader, it is in what you don't tell them.
The third principle is about suspense, which is not specific to horror; it can be applied to basically any genre. But it is, for obvious reasons, especially important in horror. And more importantly for you, the third principle is extremely pertinent for the hunter/hunted genre. It is usually the main factor in that genre.
- Don't give your readers an accurate or complete depiction of the events of your story
Writing can do something that other mediums like film have a much harder time doing: forcing the reader to imagine their own version of events. If you haven't read Edgar Allen Poe's The Tell-Tale Heart I highly recommend it. Its really short, so I suggest reading it in full, but in case you don't want to do that, I will put a short passage here as an example of how the reader's imagination gets the better of them.
Now this is the point. You fancy me mad. Madmen know nothing. But you should have seen me. You should have seen how wisely I proceeded --with what caution --with what foresight --with what dissimulation I went to work! I was never kinder to the old man than during the whole week before I killed him. And every night, about midnight, I turned the latch of his door and opened it --oh so gently! And then, when I had made an opening sufficient for my head, I put in a dark lantern, all closed, closed, that no light shone out, and then I thrust in my head. Oh, you would have laughed to see how cunningly I thrust it in! I moved it slowly --very, very slowly, so that I might not disturb the old man's sleep. It took me an hour to place my whole head within the opening so far that I could see him as he lay upon his bed.
This story is not the story of a monster; it is the story of a man. There is nothing more normal than that. But Edgar Allen Poe was able to make his main character creepier than any monster, because we know nothing about him. As the reader, we know that the events, as described, are probably wildly inaccurate, but we have no idea how inaccurate. So when the madman in the story describes himself taking an entire hour to move his head into the door in the darkness of the night, I imagine him taking an entire hour, even though we know its probably an exaggeration. In my mind, I imagine the creepiest scene I have ever experienced, the man slowly slowly slowly inching his head with the creepiest possible pace, and I imagine the lighting and scenery and face that is creepiest to me personally. Because Edgar Allen Poe robs us of an accurate description of the scene, I am compelled, even forced, to do that.
If Poe, instead, had narrated this in the 3rd person, and simply said "The man slowly, slowly moved his head into the door over the course of an hour" it might have still been a creepy scene, but it is probably not as creepy to as many people, because 1. we are now locked in to one set of events and 2. We will probably find this less believable because we aren't the ones who came up with it.
- Don't give your readers an accurate or complete depiction of the events that led up to your story
If Poe had given the events of The Tell-Tale Heart a reasonable backstory, we might also find it less disturbing. The fact that we don't know the relationship between the old man and the madman or what they look like or, really, anything at all, allows us to imagine the creepiest possible scenario for us. Maybe the evil eye is real, maybe it isn't. Maybe the madman is just a crazy person, maybe he is a serial killer, or maybe he is a spirit, maybe he's an alien or a secret government experiment. We don't know.
Because our brains are shaped by evolution, imagining the creepiest/worst possible scenario is natural because preparing for that scenario is what protects us best. Utilize that.
H.P. Lovecraft and Junji Ito (horror comic writer/artist) are both masters of this. And I would suggest reading their work for examples.
This principle is even evident in many films in the genre that you are writing, such as Alien (This isn't in a natural setting, but it is definitely a movie about hunter/hunted. Also only referring to the first film, not the series as a whole. If you haven't seen it, there are no spoilers here.). Throughout most, maybe all, of the film, the Alien is not shown in full and, the parts of the Alien that are shown are shrouded in darkness. So, in the first film, we hardly know what it looks like. We also know nothing about where they come from originally, we aren't even entirely sure what they are capable of. Do they have a home planet? Do they have a hive mind that will be alerted if this one is hurt or killed? The audience's imagination is left to fill in all of these blanks.
- Make the characters you want your readers to care about powerless, but active
In most cases, in order to have a suspenseful scene, the success of the plans that the character makes must be, for the most part, up to the whims of forces outside of their control. This does not mean they should be passive and just accept their fate or run away endlessly, it simply means that even their best and most noble attempts at dealing with the threat are reliant on chance and/or the whims of an uncontrollable force.
In The Tell-Tale Heart the segment where the madman kills the old man is really suspenseful because the old man has no say in what happens to him; he is old and probably isn't as strong or as quick as the madman. But he is active because it seems that he is trying his best and is ready to fight, even though it probably won't help at all. Also, he lacks complete knowledge like the madman, because it is dark, and it seems from the account that he was not entirely sure someone was in his room.
In the climax of Alien, Ripley is still an active protagonist (which is very important to have), she still has plans and she is the one executing them, but the success of the plans she makes are entirely determined by things like the speed of the execution of the multistep process of initiating things on her ship, the glitchiness of the ship's computers, the stubbornness and ignorance of her crew, and what the Alien choses to do and where the Alien is. Outside of her actually making the plans and choosing to execute them, she has absolutely no agency in the situations in the film.
In comparison to things like action movies, where the protagonist essentially makes new plans almost every moment in a fight or chase scene, thrillers have the protagonist make only a few plans throughout the course of the film, because there are only a few plans that are even viable, and they spend a large amount of time simply executing them. This is where suspense in the horror and thriller genres come from. The longer you can draw this lack of agency out and still keep your characters actions both active and realistic, the more suspenseful your scene will become.
If you cannot keep your characters active anymore, I.e. if your characters run out of realistic ideas of dealing with the threat, then your characters should probably die or you should revise.
TLDR; How to apply these to the hunter/hunted genre in a natural setting
Lets look at the first principle. If you are writing something that will be read in word form (as opposed to something like a screenplay or a comic), you can think about writing it from one of your characters perspective, and let their fear or maybe insanity cloud their account of what happened. Perhaps you could write it in the form of journal entries.
If you are doing a short film/comic this is much harder to do, but it can be done. Consider having characters actually just tell other characters about certain events without showing them. You could also use the technique of stopping a scene right when something terrible is about to happen, so the events are implied but not shown. You could also make it really dark, foggy, or rainy so that its hard to see exactly whats happening (I recently saw a horror film called Hereditary that just came out and used all of these techniques very well)
For the second principle, don't explain where your monster came from or what it is in great depth. Don't explain it at all if you can help it. Don't describe what your monster looks like, instead, describe how your characters react to the monster. Let their fear do the describing, figuratively or literally. "It had.. god I don't want to remember it... I don't know, I couldn't count the number of legs, it was moving too quickly. It might've had dozens, maybe even hundreds. I think I am going mad... but it might have had hands too, human hands. I could have sworn its fingers felt me."
Perhaps you could treat your environment the same way. Maybe the characters slowly find out that the natural setting they are in is not so natural, and maybe the reader never finds out why. "I was walking for hours in the dark. There was no moon that night. I remember hearing owls and crickets; and leaves in the wind. But all at once, every owl and cricket stopped making a sound, and the winds stopped too, abruptly and without warning."
For the last principle, you have to make it so that the monster has suspenseful abilities. That is 1. it should probably be vastly more powerful than your characters. 2. Its capacity for hurting the characters should be based mostly on its own unknown behavior patterns/instinct, basically based on chance. Maybe the monster can burrow under the ground, and so can basically pop out of the ground and kill you at any point and there is nothing you can do about it, you can only know it is in the general vicinity because of a clicking sound it makes occasionally. Maybe the monster poops mines that are imperceptible to sight, but you can smell them when they are near (lol). Maybe the monster can camouflage perfectly as a tree. So any tree could be the monster, and there is no way for the characters to know its hiding except the forest goes silent. The pattern is that you have to have a way of telegraphing to the readers/audience that something is about to happen (a clicking sound, a smell, a silence), without giving the characters agency over their fate as a result of that knowledge. You could also not have the monster telegraph and just tell the reader/audience things the characters don't know, but that usually works better for film than for writing.
Anyways, this was such a long post that even my tldr was long. I hope you got something out of it, and if you read this whole thing, thanks for your time.