For every random genetic change that did something that turned out to be useful, there were countless ones that did nothing useful at all or were even counter-productive (to get a sense of how many “tries” there were, consider every time every beetle in the World tries to reproduce times how many eggs they lay times several random genetic changes per egg times millions or billions of years - we’re talking grains of sand in a beach level or even more, and this is just for one kind of creature that doesn’t even reproduce all that frequently).

Then for all those random genetic changes that did something that turned out useful, there are only going to be some were that make enough of a difference in terms of increasing the survival of a beetle till reproduction and way more that didn’t make a difference.

You know what happen to all those quadrillions or whatever of tries that went nowhere? We’ll never know about them because the creatures in question are long dead (if their eggs were viable to begin with). We’ll only ever know about the ones which did work.

(There are actually a lot of cognitive falacies around how we perceive success because we only really get to know about what worked, not about the countless things that didn’t work. A good example is how most people pretty much only hear about Startups that made it big, yet for every Startup that does succeed enough to become widelly known there are tends or even hundreds of thousands that fail and we never heard about, so it might seem that Startups generally successful when the reality is, in average, the very opposite)

Continuing on the Evolution story, if the previous part of the process worked based on the Maths of “trully insane large numbers”, at this point we add an effect akin to compounding interest: even if a genetic change adds a very small increase in reproduction for an animal - say, a beetle with a given random genetic change that did do something useful and gives it a 1% higher chance of successfully reproduce - as long as that trait gets passed down to the next generation, it means (rought) that all else be the same there will be 101 beetles born with that change for every 100 beetles born without it, for every reproductive cycle. This might seems little but as I said it compounds, so for example after 71 generations that will have grown to 200 for every 100 and it will keep growing.

This is how even a random genetic change that gives even just a tiny increase in success of living till reproduction and reproduction itself will, given enough time, come to dominate a population.

And then all those slightly different beetles keep on having the random genetic changes happen (the first part of the process) and those additional changes that did work and gave a tiny bit more success over that ones with just the original change will get the compounding part of the process.

TL;DR (but you should)

A beetle with a random genetic change that affected its shell that makes it every so slightly harder to spot for predators in a place that has lots of water droplets on leaves will have more descendants than the rest and some of those will randomly get additional changes that make that effect even more successful at making the beetle harder to detect for predators thus having even more descendants than the rest and amongst those the ones with random changes that make it even better will have more descendants and so on. Given enough time and enough beetles this is how you go from beetles with a “normal” carapace to beetles with a mirror-like carapace.