The fight to take over Pioneer Square district (District Showdown) will be possible only after D.U.P. forces control less than 30% of a district. Go to the place marked with a phone icon (large billboard on the rooftop) and make a call.
All enemy forces should appear on a highway - which is big advantage. They won't be able to reach Delsin, so initially you should attack them from a distance trying to blow up armored vehicles. After that move closer to the highway and use some attacks from the air like Comet Drop. Watch out for a single soldier with minigun - you have to weaken him down and them finish him after he creates a shield.
Rewards for taking over Pioneer Square are:
- Unlocking fast travel
- Getting rid of all D.U.P. soldiers in the area
- Unlocking Delsin's unique clothes - R.I.P.