Ah, my legion. I admit that I didn't like Giffen's experimental style. His older stuff is much better.
Lessee...
The Legion of Super-villains has invaded a sword-and-sorcery type world, where they probably ordered the slaves to make that Mayan-style disc. They talk evil stuff.
Micro Lad has stunningly bad luck to rob the casino planet that Dream Girl and Star Boy (nowadays StarMAN) are vacationing at. The Legion of SuperVillain's teleporter rescues Micro Lad after Shrinking Violet is called in to find him. Violet has a grudge because Micro Lad previously kidnapped her, put her in sensory deprivation, and had her replaced by a shapechanger.
The couple talking about restoring a world are Mon-el and Shadow Lass. Mon-el was named that because Superman thought they were related, so the 'el' is honorary. He's actually a Daxamite (same powers as Kryptonians, except their kryptonite is lead) and this is Daxam, which was conquered by Darkseid in the Great Darkness Saga back when New Gods were still rare. Darkseid mindcontrolled the Daxamites and altered their sun to give them powers and terraformed the ENTIRE PLANET to look like his face. The Legion is helping re-terraform the planet. Shadow Lass is, incidentally, the same race as the Sinestro Lantern who is chained to a book of scary stories.
The naked chicks are on Light Lass' (Ayla) home planet of Winath, where she's been hiding since she decided superheroing sux. Almost everyone on the planet is twins. And nudity is acceptable for farming. Sounds like a fanboy dream!
The Legion of Super Heroes arrives by spaceship on Takron-Galtos, the prison planet. The short kid with heat vision is Ol-vir, previously described as a child who worships Darkseid. Can't remember if he's Kryptonian or Daxamite. He's broken out of prison and sacrifices an alien guard to Darkseid. Ron-karr is a punk. Ultra Boy has Kryptonian level powers, but usable only one at a time. The Legion of SuperVillains teleports many of the criminals away and blocks the Legion of Super Heroes attempts to follow.
Ol-vir needs to come back! He was Superboy Prime level annoying, but not all-present.