The great cosmic villain Despero first appeared in the DCnU New 52, as far as I know, with Justice League #19, so it is hard to know how much of his story is canon and how much has been tossed into the dustbin of editorial Crises. But let’s try for what we can, shall we?
Despero first appears to comic book readers during the Silver Age, when in pursuit of two rebels from the planet Kalanor, which he rules as a tyrant.(Pre-Crisis, it is a dimensional solar system). They are attempting to create a weapon to defeat him. The rebels make contact with the Justice League of America(the real one) due to the Flash, with him accepting Despero's challenge after he places the rest of the group in a hypnotic trance. The Flash is defeated, however, in a game similar to chess due to Despero cheating and using his third eye's mental powers. Along with the rest of the JLA the Flash is sent to another world.
Despero found out about this by reading the mind of one of the rebels he had tracked down and teleported, though her father and Flash were protected by the dimensional traveler’s “blue glow.” However, the JLA are able to escape all the dangers on the worlds and return to Earth using a dimensional traveler one of Despero's henchmen possesses after the Flash defeats him. Despero has found the rebel and plans to use their energy-absorbing weapon they hoped to use to disable his weapons to conquer Earth. But Snapper Carr (bring back teen mascots!) uses it to weaken the villain after pretending he has been hypnotized, though the “blue glow” protected him. Despero is then imprisoned and Kalanor is freed.
The villain has his third eye surgically removed, making him lose his hypnotic powers. Eventually it grows back, he fakes his death in an explosion at a lab and in revenge ages half of the Justice League and banishes the remainder to three other worlds, where he has caused reptile, insect and marine life to become intelligent, planning to conquer the worlds later.
When Despero attempts to deceive Wonder Woman by disguising himself as an aged Superman, she overpowers the villain with her lasso, realizing the energy should not have affected Superman, and forces him to undo his actions. Despero is thwarted again when the Justice League intervenes in his intergalactic plans of conquest, and save the Martian Manhunter who is being forced to play in a life-and-death chess match. (Despero must have been a member of his high school Chess Club!)
Despero eventually returns with even greater abilities, and completely destroys the Justice League satellite. After defeating the League, Despero reshapes GothamCityto suit his purposes. Taunted by Batman, Despero is eventually distracted, allowing fellow member Vibe to extinguish the "Flame of Py'tar," the source of Despero's power. The villain's form is immediately dispelled and reality restores itself.
The cosmic foe eventually reforms, and targets the Justice League member Gypsy. After murdering Gypsy's parents, Despero is about to kill her when the Martian Manhunter intervenes. The villain quickly defeats the Manhunter, although fellow Justice League member Guy Gardner arrives and hurls Despero away.
Despero attacks the League at their headquarters, and kills the comatose Steel (on life support for injuries sustained during a battle against the androids of Professor Ivo). When Despero is about to murder the Blue Beetle, the Martian Manhunter bestows upon him the gift of "Mayavanna": a sacred Martian rite that provides the subject with a reality in which they obtain their desires. Despero sees himself killing the entire League and destroying the world, and is immediately at peace. The villain is then reverted into a fetus, and is eventually given to trader Manga Khan in exchange for his servant robot, L-Ron.
A re-aged Despero is angered by this defeat and escapes from Manga Khan, returning to Earth to battle the Justice League (again??). Unknown to Despero, Kahn hires the bounty hunter Lobo to recapture him. Despero engages the Justice League, Justice League Europe and Lobo in Times Square, NYC, and keeps them all at bay. A desperate Green Lantern Kilowog and L-Ron use the slave collar Despero still wears to switch minds with L-Ron, with the diminutive robot's body being destroyed shortly afterwards. Now in Despero's body, L-Ron returns to Manga Khan. L-Ron reappeared, still in Despero's body, and had a number of adventures with the Justice League Task Force and Justice League International.
Meanwhile, Despero later returns in spirit form and temporarily repossesses his old form until stopped by Supergirl. The villain makes a second attempt to return to a corporeal state, possessing the Martian Manhunter. The team Young Justice, however, use the Manhunter's fear of fire against him and team ally the Secret banishes Despero's spirit form.
His spirit eventually returns with the aid of JSA villain Johnny Sorrow and takes over the body of Lex Luthor, then President of the United States. Together they release the Seven Deadly Sins (an iteration of which is soon to be seen in DC’s Trinity War event) which possess several members of the JLA and JSA, and neutralize the wizard Shazam (not to be confused with Billy Batson’s alter ego today).
The remainder of the teams successfully drive the Sins from their comrades, and eventually defeat both Sorrow and Despero, who is driven from Luthor when exposed to Sorrow's lethal stare. The villain returns as the guiding force behind a new Secret Society of Super Villains and allows them to remember they once learnt the Justice League's identities. Although Despero takes mental control of several of the League, he is eventually stopped by Green Lantern and imprisoned on the planet Oa.
Having allied himself with a race that destroys species unworthy of survival, Despero attempts to convince them to destroy Earth by using an alien substance known as the “Blackrock” to influence Earth's alien superhumans – the Martian Manhunter, Supergirl, Starfire, etc. -- to turn against humanity by playing on their occasional feelings of isolation. However, his efforts are foiled when Batman exposes himself to the Blackrock while under attack by Superman, the sight of his friend's contamination helping Superman to recognize what is happening to him and allowing Superman to confront the aliens directly and convince them that Despero deceived them.
Despero returned in his original human form when plucked from the timestream by Mister Mind, and is convinced to join a group called "The Time Stealers." The villains successfully create an alternate universe that differs significantly from the original. Hero Booster Gold and several allies (Rip Hunter and the JLI) eventually undo the change and restore the original universe. (After a million reboots, isn’t it getting hard to tell what “original” is, or even “extra-crispy”?)
The former tyrant briefly allied with villains Morgaine Le Fey and Enigma and became god-like until stopped by the combined efforts of the Big Three (Supes, Bats and Diana). Despero returns (as always!) to attack the Justice League but, when teleported away by Zatanna, is imprisoned on Oa once again.
At the request of human computer Vril Dox, Despero joins in the fight against the original Starro (a humanoid) that controls all other versions and is conquering the galaxy. Despero engages Starro in combat and although easily destroyed begins to regenerate into a superior form, which was always the villain's intent. Vril Dox uses Despero's still-living head as a weapon against Starro and its forces.
Now, assuming without most of this baggage, he has reappeared on the doorstep of the Justice League in the New 52. We will have to see what newbies Firestorm and the Atom have to say to him!