Hey Nexo, cool game !
You mean the trespasser event? It's not really tied to the Outskirts, it can be triggered anywhere.
All you have to do is keep the bar as close to the limit as you can, without letting it overflow. Each time you press the action button, the bar decreases along with your stamina, if you run out of stamina you can't manipulate the bar anymore.
If you let the bar overflow 3(?) times, you lose.
Be aware that Stamina Regeneration is a sub-stat derived from AGI, so if you're having trouble with stamina in this event, your AGI is probably lower than it should be