Ares used the Annihilator to help the military forces of East Kasnia defeat those of their enemies, the West Kasnians. It was incapacitated by Hawk and Dove (with the aid of Wonder Woman) who were able to convince the two sides to stop fighting, robbing it of it's source of power. The intert construct was stored in a secure facility onboard the second Justice League Watchtower.
Project Cadmus wanted to use the Annihilator as a weapon against metahumans. They recruited "Task Force X", a group of supercriminals to retrieve it. Under the command of Colonel Flagg, Deadshot, Plastique, the Clock King, and Captain Boomerang infiltrated the Watchtower and stole the construct.
At Cadmus headquarters, Tala made numerous failed attempts to remove the Annihilator's "Achilles' heel". Seeing no other option, she consulted with the spirit of Felix Faust, who at that time was trapped in a mirror. Felix tricked Tala into releasing him from the mirror, imprisoning Tala in it herself.
Faust proceeded to possess the construct, intending to use it to gain revenge upon the god Hades for betraying him. Annihilator-Faust easily defeated the Amazons guarding the gate to Tartarus and captured Hades, chaining him to a stone in a swamp where he was continuously fed upon by vultures.
Learning of this, Zeus decreed that Wonder Woman was to restore Hades to the throne of Tartarus. She recruited the assistance of Hawkgirl and freed Hades from his torment. The three then defeated Annihilator-Faust, destroying the construct in the process.
It should be noted that the Annihilator construct bore a striking resemblance to the Entropy Aegis, a suit of armor forged from the shell of a defeated Imperix drone by Darkseid and worn by John Henry Irons (alias, Steel) during the Imperix War in DC Comics main continuity.