Update:
As of February 10th 2021 this achievement is broken.It's busted on multiple platforms but should at some point get patched and working again as has been the case with multiple other achievements. Once it's working feel free to consult the guide below.
The achievement currently has the wrong description when viewing it while locked, it should read "
In public matches, get a total of 500 successful Skill-Checks."
Viewing it while locked has the same description as the "Zealous" achievement but that is wrong, you don't need 8k blood points for this achievement. Despite being the wrong description, it still goes up for the actual intended criteria which is for getting the skill-checks.
Skill checks will pop up when you're either repairing a generator, sabotaging a hook/bear trap (Bear traps only show up when the killer is the Trapper) or when you're healing another survivor/yourself.
The skill check is a giant circle with a small section marked randomly on the circle. Press
when your line that moves clockwise goes into that little section and you'll be awarded some points for the successful skill check.
Screw it up by being too fast or too slow and you lose some of your meter and a secondary negative effect.
If you mess up a generator, it will alert the killer with a map wide visual queue.
If you're sabotaging and screw up then you'll just make a loud audio noise within a small radius but you won't alert the killer with a map wide visual queue.
If you screw up the heal then the character being healed will scream but again it won't have a map wide visual queue.
You'll also notice a giant white bar at the beginning of the skill check area. If you hit that then you get 100+ bonus points for the objective, boldness or altruism category depending on if you're repairing a generator, sabotaging or healing respectively but you're more likely to screw up trying to get those by pressing the button too early so just try to hit it after and forget the bonus points.
Various tools, tool add-ons and perks can make it easier for you to get skill checks.
Assuming the killer isn't killing you right off the bat every time, then you should be getting several skill checks done every match.