~Complete a district showdown~

To unlock a district showdown you must bring the enemy control within a territory below 30%. This can be done by doing side activities and finding collectibles. Each district has one showdown. It's basically a final fight against the D.U.P. Agents that are stationed in the district. Finishing such a showdown will make most enemies in that district disappear, but also unlocks a fast travel point. You should wait with this until you have done the combat related trophies so you don't have to get them in your next playthrough.