Within every district there is a phone icon. These represent the District Showdown missions. These are unlocked once the District D.U.P population is 30% or lower.
You unlock this by doing other missions and collecting blast shards within that district to drop down its percentage. Once you do that, simply start the showdown and take out the D.U.P forces that will attempt to attack you.
Once you have done so, the trophy should unlock after you unlock the fast travel for that district, and other game features.