Quickly go for the couplings while taking as little time as possible on defensive units. If you take your time destroying them and go on to other couplings, the couplings will be repaired and defenses will be reinforced. Right after their destruction, go to the center and destroy defenses. Hide under the platform to recharge your armor. Once the defenses are substantially diminished, go to the top and strafe Horgan, keeping the cannon below and in front of you. When he charges his attack, drop behind the cannon so that he will hit it and damage it. After a couple times of doing this, not only will you defeat Horgan but also get the hero objective of destroying the cannon.
Unlock the following armor suits by performing the corresponding tasks:
HOW TO UNLOCK
Complete the "one man army vs. mercs" challenge, which is unlocked after story mode mission 7.
Classic Mark I
Complete the "one man army vs. AIM" challenge, which is unlocked after story mode mission 8.
Complete the "one man army vs. maggia" challenge, which is unlocked after story mode mission 4.
Complete the "one man army vs. AIM-X" challenge, which is unlocked after story mode mission AIM-X. Hulkbuster is slow but can sustain massive amounts of damage. Its Repulsors are more like cannon shots and in place of grenades or missiles is a single cannon shot that hits a target, then a moment later creates an explosive shockwave that is devastating to large groups of enemies.
Complete the "one man army vs. ten rings" challenge, which is unlocked after story mode mission 3.
Ultimate Suit(PS3 exclusive)
Complete story mode. The Ultimate suit is the equivalent of the Extremis but does not have stealth has a more powerful Unibeam and Gatling Repulsors that are weaker.
At the fortress' jamming device, next to it is a door mounted to the bottom of the fortress. Fly up inside and destroy the four boxes that will take down the shields of the cannons. Fly back down. Go around and fly to the highest point. Take out the cannons with your missiles. Jarvis will tell you to go inside. Tap into the computer and come back out, then destroy the four engines and the top of the craft. Go back inside to another door, then open the big loading bay door and fly inside. There may be a couple mines dropped on the city below. Destroy the mine and go back into the loading bay doors, then destroy the big blue cannon to go inside. Straddle between the two orange power engines to complete the level.