Play the game until you reach Dead City. You'll know you're in the right place when you see a cutscene where Cat hisses at and runs from a bunch of small, ugly, but very numerous bugs. This triggers a short run segment where you have to evade the bugs for about a minute until you reach safety by jumping over a gap and through an open window.

Here's the important part: if a bug manages to jump on you or latch onto you, you can shake it off. But for this achievement, you need a perfect run. You must make it all the way from the start of the run to the open window without any bug connecting or latching onto you. If you ever see the prompt to shake a bug off, hit Esc/Start and restart from checkpoint.

The bugs spawn at set places and times, but their behavior is not entirely predictable. There's high variance in which ones will jump at you, when they'll jump, and at what angle or height. Using the exact same tactic twice can result in vastly different outcomes.

With practice, you will learn through trial and error and get better. But be prepared for inconsistency.

After about 30 to 50 attempts, during several of which you'll have miraculously succeeded in parts you were struggling with before, only to then get caught by a magically homing, lightning-fast bug in an easy section, you'll start wondering what you're missing. This is normal. Don't be alarmed.

The trophy is insanely difficult and heavily RNG based. Struggling with it does not mean you're a bad player or a terrible human being.

Recommended Guide: Darkhowl Gaming has a pretty thorough breakdown of how to maximize your chances. Full disclosure,I'm not affiliated with that channel. It's simply the most helpful guide I was able to find.

The "easy way" title is obviously dishonest clickbait, but that's par for the course on YouTube. The actual breakdown has merit, and it starts at 2:47. Skip to that timestamp if you want to get straight to the helpful info. And by all means, don't take it as gospel. Peruse and search for a wide variety of tips and tricks from all sorts of other sources.

Now you're properly armed to tackle this challenge. Go back to the game and bring out your god tier gaming skills.

Focus.

Breathe.

Remember.

Execute.

You can do this.

One hour and 100+ tries later, you'll be exceedingly frustrated and tired of this.

Take a break. Go walk your dog, or pet your cat, or chat with your loved ones. Come back to the game later once you've put the salt behind you and give it another go.

Another 90 minutes and 120+ attempts later 10 of them close, you'll come to a realisation:

This is not worth your time, nor the aggravation.

This "challenge" is merely absolute nonsense, and you're getting frustrated and annoyed for no good reason. The devs simply didn't test it or think it through properly before implementation. There's an enjoyable game to play behind this absolute garbage. You should not waste a minute more on this RNG-based nonsense.

Open up your favorite search engine and type the words "steam achievement manager" in the search box. The first URL should be a GitHub page where you can find the code and a download link for the program of the same name.

It's a simple ZIP file. Download it, unzip it wherever you feel like, then run the application.

Instructions:

You'll see a list of your Steam games. Scroll down until you find Stray.

Double-click the game's icon. This opens up a list of the game's achievements.

Scroll down until you find "Can't cat-ch me."

Tick the box to the left of that achievement.

Hit the "Commit Changes" button in the top right corner of the application.

Exit the application. Delete it from your computer if you like.

This is obviously a bit of a rant guide, but it's not just that.

I genuinely, strongly recommend that even completionists and achievement hunters do not bother with this. I have used Steam Achievement Manager a grand total of twice in the entire time Steam has existed: once for a bugged achievement I had met all requirements for but which refused to unlock, and once for this. It is THAT bad.

How much you practice does not truly matter. Gitting gud does not truly matter. Strategy does not truly matter. One can easily fall under the illusion they do, because they help, a little bit. Spawns are fixed, so smart positioning helps. But the skill cap is, in truth, very low here. All working strategies are woefully unreliable. Enemy behavior is simply far too random, and the result is that what getting a perfect run truly requires is absolutely insane luck and RNG.

TL;DR

This achievement is godlike-tier garbage. You should not waste a single minute of your life on it. Move on to the rest of the game, or to a different game, or to something else in your life.

GLHF.