29 years ago - Maxima is born the scion of the Blood Royal of Almerac.
8 years ago - 21-year-old Maxima is manipulated by Brainiac to declare war on earth. Superman stops her, and together they battle the Brainiac worldship.
6 years ago - 23-year-old Maxima comes to Earth to take Superman as a mate. He refuses, but helps her quell an uprising on Almerac. She leaves the throne to her advisers to go to Earth and repay her blood debt. She joins the Justice League.
5 years ago - 24-year-old Maxima is the last member of the Justice League to fall to Doomsday. After Superman's supposed death, she returns to the Almerac throne.
Ridiculous costume aside, I love Maxima. The idea of an intergalactic princess that is so badass she gives Superman a run for his money who then decides she's going to take him as a mate is just the best. It's all those ridiculous "Superman's girlfriend" comics, but with a character that can punch a hole in a tank. She's not a character that needs to be in the Justice League for long, especially since she's basically only there as a favor to Superman, but the fact that she's there at all is just great.
Maxima's Comic History
Maxima was created in the late 80's in the thick of the post-crisis years of the Superman books. It's a very fun era to get into, because the mythology was being completely rewritten within the new DC timeline, and a lot of it worked really well. Maxima was a creation of Roger Stern and George Perez, first appearing in Action Comics #645 before really showing up #651. She's a super-powered alien warlord who comes to Earth specifically because Superman is her ideal mate, and winds up attacking him when he rejects her.
The story is completely wackadoodle, but It's also a lot of fun. This is happening right in the middle of the X-men absolutely dominating the entire medium, and the stylistic influence is obvious. You could certainly make an argument that the story concept is problematically sexual, although it's probably more a question of personal taste. The main thing Maxima offers Superman is the fact that she can successfully bear him children, while a human probably can't, and that's certainly a valid conceptual question to bring up in the context of Superman's larger mythology. It's being brought up in the person of a highly sexualized femme fatale character, but these ARE comics we're talking about.
Maxima would appear again in the massive Panic In The Sky crossover, and would go on to become a member of the Justice League during the Dan Jurgen years. This means that she was among the Leaguers to battle Doomsday, where she made a very impressive showing. From there she became a member of the spin-off book Extreme Justice, and sort of rode the wave of the decline in popularity of 90's era characters. She's now a regularly referenced part of Superman's mythology.
Our Maxima Story
The core story beats we want to use with Maxima are her original introduction as a pseudo-antagonist for Superman, her participation in the 'Panic in the Sky" arc where she joins the fight against Brainiac, and her time with the Justice League where she fights Doomsday.
The biggest change we made was the order of events; here, here the Brainiac battle is actually her first interaction with Earth. As one of the few people in the galaxy that can actually give Superman a run for his money, she would be an ideal weapon for Brainiac to manipulate into attacking him. She doesn't necessarily need to already know who Superman is for this to happen.
From here, now that she knows who he is, NOW it makes sense for her to return to Earth and expect Superman to be grateful for the offer to be her concubine. We borrow a little bit from the Maxima episode of the Superman animated series, by having this story resolve with Superman helping her quell an uprising on her home planet. We'll use this as the reason Maxima returns to Earth and joins the Justice League entirely as a way to pay her debt to Superman.
I'm actually really torn here. On one hand, There's a pretty basic argument to be made that any character whose design is so obviously overtly sexual is just too much, that the character is made better if you give them a more reasonable costume. This is especially true of a lot of 90's characters, when comics were really striving to new levels of sensationalism. This is definitely the route the Superman Animated Series took, giving Maxima full-body armor that looked like something Jack Kirby might have come up with. This certainly proves that you can do Maxima justice without having her fight in weird swimsuit-armor.
On the other hand; there ARE characters where there's a balance to be made with the sexuality of the character. Wonder Woman and Starfire are obvious examples. Both characters' looks are iconic, and a huge part of that is their sexuality. Just like both of these classic characters, Maxima's costume becomes a problem when the sensationalism of her look becomes the focus at the expense of their actual characterization. She's an obviously sexual character and her swimsuit-armor actually works pretty well with that story. We just don't need that to devolve into cheesecake.
In the comics, after the death of Superman, Maxima continues to serve on the Justice League and it's spinoff Extreme Justice team. In our story we actually don't need her to stick around; and since she was only serving on the Justice League for Superman in the first place, it makes sense that she would return to Almerac.
From here, the next story she'll be a part in is our new Omega Men team. As Adam Strange brings together heroes from different planets to stand against the galactic invasion by the forces of Lady Styx, Maxima is an obvious candidate to join him. With her inclusion the level of power on that team really jumps up quite a bit, and it's going to be pretty awesome to see what they can do together against waves of alien bad-guys.
Once that story is resolved, Maxima is back to simply serving as the scion of Almerac's Blood Royal. Apparently, back before Dan Juergens brought Maxima into his Justice League, writer Jerry Ordway was planning to make her the new leader of Warworld. That's a very interesting story idea that has real legs. Currently Warworld has been retaken by Mongul and is involved in the coming invasion of Earth by Zod's forces, but once that story is resolved having Maxima and Almerac come into conflict with the newly leaderless Warworld could be a very cool direction to take in the future.