Oldest child of the Royal family of the planet Almerac, the fiery-tempered Maxima came to Earth in search of a suitable mate, leaving behind Ultraa, her betrothed. She and Superman are genetically compatible; she could give him what no Earth woman could - children. She was infuriated when Superman rejected her offer, saying he had no desire to father despots.
Maxima later found herself reluctantly working with Brainiac who had destroyed Almerac with the Warworld. She turned against him, and helped Earth's heroes defeat him, subsequently joining a reformed Justice League for her own reasons after the League saved Almerac from Starbreaker. As a Leaguer, she helped in the fight against Doomsday, and when that version of the League disbanded, she became a member of Captain Atom's Extreme Justice. She considered both Captain Atom and Amazing Man as potential mates, but neither were interested. During the period of her flirtation with Captain Atom, an angry jilted Ultraa attacked him, Maxima eventually stopped the brawl and sent Ultraa back to Almerac.
She offered herself to Superman again, hoping that her recent good deeds would offset her earlier ruthlessness. Superman, now married to Lois Lane, was even less interested in her proposal than before. Angry and humiliated, she joined the Superman Revenge Squad. She swore that Superman had rejected, humbled and humiliated her for the last time, and threatened that the next time they meet, it would truly be war.
However, in her next appearance, during the build up to the Our Worlds at War crossover, Maxima and the 'Chosen People of Almerac', as she phrased it, showed up in Earth's solar system where they met up with Superman and fellow JLA member, Green Lantern. Superman and Green Lantern were just beginning to investigate the disturbing disappearance of Pluto and the even more distressing engine ion trail associated with Warworld, when they stumbled across Maxima, her people, and the supervillain Massacre.
After a battle full of wounded pride, Maxima eventually conceded her position when Almerac's rendezvous showed up using a Boom Tube. She explained that she was leading her people to safety from Imperiex, the force that conquered her world. Massacre had seemed to meet his death, however, somehow Maxima came across him and described her association in these words: "Massacre serves only me now." To save her people, she allied herself with Darkseid's son, Grayven, who was taking them to regions unknown. This was also being undertaken without the knowledge of Darkseid. Maxima left Superman with the following words: "Mark my words, when Imperiex comes for your precious homeworld, you'll see alliances you've never dreamed of."
All that Maxima warned eventually came to fruition as she and a myriad of other characters (both heroes and villains) formed alliances with Earth and Apokolips in an effort to destroy Imperiex.
Maxima ultimately met her demise in an heroic effort to put her ship between the destructive beams of Brainiac 13's Warworld which would have resulted in the destruction of the entire universe.