You must play through Story mode to unlock three different powers. There are four total powers, and they are marked with the following colors on your mini-map:

Concrete - Grey (fallen enemies; only available after completing Story mode)
Neon - Purple (neon signs)
Smoke - Brown (chimneys, destroyed vehicles)
Video - Blue (satellite dishes, TVs, and other screens)

To change powers, simply consume the respective power source. Look for a single enemy or kill a group of enemies, and leave only one alive. Then, shoot that enemy one time with each power, and kill him. If you have already cleared all areas of enemies, you can still get the "Hat Trick" trophy by waiting for a DUP Raid (shown with red circle on world map), or look for a patrolling vehicle.