This achievement seems to have a bit of a misconception behind it. You don't have to be all that close to trigger a fight.
Thugs, Yakuza, Gangsters etc. will occasionally be standing around looking to pick a fight. As you play you'll start to notice which character models are your enemies (however sometimes they aren't looking to pick fights especially if they're carrying a shopping bad. Even if you know it's an enemy character model the shopping bag will be a dead give away they aren't looking for a fight.)
When you see someone ready for a fight, keep enough distance away to where they won't immediately sprint offer you and click
to enter first person.
Now just stare at them for a good 10 - 15 seconds and eventually they'll get bothered and comment on how you're staring at them.
If the fight isn't triggering just get a tiny bit closer. If you get too close they will run at you to which you can run away and wait for them to return to where they are standing. You shouldn't need to get that close however just have patience as you stare them down.