Here are the 7 hidden objectives.

Survivor - Mission 1 / Survive the initial wave of Cybran attackers without losing any units.
Economic Opportunist - Mission 2 / Build at least two Mass Extractors in enemy territory.
Master of the Seas - Mission 3 / Build an Atlantis II Experimental Aircraft Carrier.
Brutal Conqueror - Mission 4 / Defeat Coleman without the aid of the Fatboys.
Experimenter - Mission 5 / Build at least four Experimental units
None Shall Pass! - Mission 6 / Prevent any enemy King Kriptors from crossing the main fortress bridge.
Nuke King - Mission 6 / Launch your first nuke.