...heroes like Supergirl, one of the alien versions of Starman, and the Legion of Super-Heroes, before his final defeat facing Superman, Batman, Wonder Woman and Robin.
Let's take a look at the history of Mongul...
The Key That Unlocked Chaos
This would give the alien conqueror Mongul control of the Warworld, a highly destructive planet created by the Warzoons, constructed to move across the cosmos and cause chaos!
Mongul was able to get control, and the Martian Manhunter blamed Superman for new weapon, and how he would now be a thread to the universe.
The heroes find that the weapons of Warworld are strong enough to hurt Kryptonians, and come up with a desperate plan to have Mongul use all the bases' weapons against them....which does work, stopping Mongul and destroying his control over Warworld, but sending Supergirl hurtling across the universe, reaching speeds she had never before.
(Superman resolves this problem in the next issue with the help of the ghostly guardian known as the Spectre, but that issue didn't feature Mongul).
Whatever Happened To Starman?
This time, Mongul is even more ruthless, killing the sister of Prince Gavyn (the Starman of Throneworld, no relation to the original Starman of the JSA at this time), and marrying the Lady Merria to take over this world.
Superman arrives and meets this Starman for the first time, and the two work together to defeat their foe...
...and Starman learns more of his power and place in the universe.
In Final Battle
A small contingent of Justice League members, including Green Lantern, Red Tornado and Black Canary, along with Supergirl, were unable to defeat Mongul, so Superman took the battle upon himself. The Legion of Super-Heroes came back to the present from their 30th Century future (not concerned with damage to be done to the timeline, since the Earth hadn't had its sun eaten by the Sun-Eater), with Legionnaires Cosmic Boy, Brainiac 5, Sun Boy, Element Lad, Shadow Lass and Wildfire facing off against the 20th Century Sun-Eater (and being able to stop it, without losing a teammate like they did last time).
For The Man Who Has Everything
This time, Mongul attacked Superman on his birthday, in his Fortress of Solitude....by giving the Man of Steel a gift, a plant called the Black Mercy, which parasitically attaches itself to a person, gives its host visions of an ideal life, as it slowly kills the person its attached to.
That's how Wonder Woman, Batman and new at the time Jason Todd version of Robin find Superman, and while Wonder Woman fights Mongul, Batman and Robin try to find a way to get the Black Mercy off of Superman, which they did and defeated Mongul, all in time to celebrate Superman's birthday.
Mongul even reappeared in the new DC Universe, running Warworld, fighting a Superman in exile from Earth, and even menacing the Green Lantern Corps.