Let me also expand detail ways to detect them since I alluded to it and you seem to need the help;
It may be worth also detailing the stealth system a bit to start.
It actually works the same way both for the player and NPCs. It's not a raw check of your detection vs their stealth, there are factors that play into it and it comes in a gradient.
In the same way that NPCs will have the eye above them that goes from green to red, you essentially do the same thing to them. Even though you may not have the detection to see them from far away, you can often "perceive" them. Think of "perceiving" something as being that orange eye. You are pretty sure something is there, but you aren't 100%. When you "perceive" something, it will actually show up as a dark outline of whatever it is, so if you're careful you can "spot" death stalkers / crawlers without actually outright revealing them.
This is actually really useful because in this state (provided they also don't detect you) the NPC won't start combat, giving you the drop on them.
Another factor is facing. If I am facing forward and looking toward the rear-end of a stealthed Death Stalker, I'll detect it much more easily. The opposite is also true. If I am facing away from the Death Stalker and it is looking right at me, I will most likely be taken by complete surprise, even with high PER.
Lastly, time. The longer you sit still and observe an area the better you may be able to detect things around you. If you suspect a stealthed enemy, slowly approach and wait a while. Remember how stealth works the same for you and NPCs? Waiting a bit allows that eye to fill up and possibly go to the next level.
So now on to how to detect Death Stalkers.
Should the above method fail you, there are still many options.
If you suspect a Crawler / Death Stalker at a certain spot (or you know its there but cant see it) simply toss a flair or your explosive of choice over there. Any throwable (minus throwing knives) works for this. I have found that Molotovs, Nail Grenades, and Stingball grenades work really well for this purpose.
You can also bait them into a trap. See, Death Stalkers and Crawlers are just stupid bugs and will happily walk over damn near any trap, even caltrops. Set your trap of choice (preferably at a chokepoint) make some noise, then wait for the stupid little bugger to walk into it.
If you're a real Alpha-Chad, you can even Yell them out of stealth. Way cool.
If you get stung and it goes through, don't panic. If its a crawler, simply take an antidote and go after it.
If its a Death Stalker you'll need to act quickly. The animation that plays after they sting you isn't really indicative of what happens. It seems to imply that the creature is gone, but what they really do is restealth right in front of you. With that in mind you can try and locate the Death Stalker before you are stunned.
You can make your best effort via employing the methods above, or even attempt to bump into it as I am prone to doing. If you don't like your chances of finding it, run as far away as you can (if you have really high MP maybe dial it back a bit) and get into a chokepoint. Most of the time the DS will not reach you until after you recover from the stun, often times being right in front of you or really close. Simply walk forward and BAM, Death Stalker!
That's kind of a meme-tier way to do it and it doesn't really work on groups of them so your results may vary.
I hope this is helpful to you and any other new players that may be having trouble with the creepy crawlies.