Read Prima's free inFAMOUS: Second Son walkthrough.

To begin this mission, head to the Space Needle, indicated by a large star with a square around it on your radar. Walk into the on-screen indicator and press Up on the directional pad to start the mission.

Use the nearby ladder to climb up to the first platform. Climb onto the rooftop vent, use your Smoke Dash and launch onto the wall above you. Climb the wall to find another rooftop vent. Use this vent to launch yourself into the air, using your Hover or Smoke Dash when you reach maximum height to grab the ladder in front of you. Continue to ascend the Space Needle until you reach the observation deck. There are several D.U.P. guards here, so work your way around using the two-piece barricades for cover. When all the enemies are down, use the vent to reach the top level of the Space Needle.

This isn't exactly a boss battle, more like training for upcoming boss battles. Work your way around the Space Needle, using Smoke Dash to avoid the D.U.P. attacks while returning fire with your Smoke Shot. Keep in mind you have the Cinder Missile, a great option considering there are no civilians up here. 

Tip: Keep moving at all times. A mobile target is much harder to hit. Use melee attacks to take out some of the regular D.U.P. agents.

When everyone is down, destroy the Core Relay and absorb the Orbital Drop power. You will have three new objectives on your screen, each one a downed D.U.P. agent that requires subduing. When you are done with all three, use the Orbital Drop as instructed on-screen. This will knock out the D.U.P. Comms Center setup on the Space Needle as well as end the mission.