To unlock other Iron Man suits all you have to do is complete the One Man Army missions which are unlocked throughout the game.
You'll have to beat 80 enemies within 10mins to unlock a new suit which can be used in mission archive or again in One Man Army.
As you unlock parts to your suit in Story mode, they will become usable in past missions in Mission Archive mode.
Complete the indicated tasks to unlock the following suits. Story mode missions will unlock One Man Army missions. One Man Army missions will unlock specific suits for the One Man Army missions.
Successfully complete the game.
In One Man Army missions, take out as many air units as possible quickly, especially jets as they are too fast to chase and difficult to shoot down. This is especially true in Arctic Battle or the One Man Army Mission 3 (vs. Mercs), as the jets are difficult and required to complete the mission. Take them out as they fly off the runway to defeat them effectively.
As you unlock parts to your suit in Story mode, they will become usable in past missions in Mission Archive mode.
This is a very challenging mission, with anti-air defenses everywhere. Immediately go for the couplings. Take 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. Immediately 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. He will hit it and damage it. After a few times of doing this, not only will you defeat Horgan but also get the hero objective of destroying the cannon.