From Bulbapedia, the community-driven Pokémon encyclopedia.
Darkrai (Japanese: ダークライ Darkrai) is the true main antagonist of Pokémon Mystery Dungeon: Explorers of Time and Explorers of Darkness and Pokémon Mystery Dungeon: Explorers of Sky. Though he mainly appears in the post-ending plot, he is revealed in the end to have orchestrated the events of the entire game.
Although normally genderless, this Darkrai is referred to as a male, but during gameplay, it is still treated as genderless.
In the games
Darkrai first appears disguised as Cresselia in the player's dreams, telling them that they are causing a distortion in the fabric of space that could plunge the world into darkness and never ending nightmares. He tells them this is because they came from the future and thus shouldn't exist in this place and time. When Azurill falls into a never ending nightmare, Wigglytuff's Guild has the player and partner go to find a reformed Drowzee to send them into the young Pokémon's nightmare to find out what's wrong. There, they encounter Cresselia, who tells them the same as the player was told in the dreams as well as blaming them for Azurill's nightmare and tries to destroy them but is interrupted by Drowzee and flees.
The partner is discovered to be having similar dreams, only being told it was because they'd been to the future and came back that's causing the distortion. Now very confused and upset, they decide to go see Palkia for an explanation. However, before they can do so, Palkia arrives in their base and takes them to his domain, the Spacial Rift. He then attempts to destroy them, claiming they're distorting the fabric of space. The two manage to defeat it in battle, however, it then becomes trapped in a nightmare. Cresselia then takes them into Palkia's nightmare where he tries to destroy them using Palkia, who he told the team was purposely distorting space. Palkia soon begins questioning Cresselia's claims however, and before the player and partner are finished off, a second Cresselia arrives and exposes the first "Cresselia" to be Darkrai, who she'd been pursuing for a long time. Darkrai then tells them that he was the one distorting space. Darkrai escapes but offers them the chance to stop him at Dark Crater.
At Treasure Town, Cresselia reveals Darkrai was the one behind the near destruction of Temporal Tower and thus causing the dark future the player came from. He was seeking to make a dark world that he could rule as his own. Although Cresselia confesses that the player and their partner existence does cause some amount of distortion as Darkrai claimed, it is not large enough to be a threat on its own; Darkrai had blamed the expanding distortions he caused on them in an attempt to destroy the team because they stopped his last plan and stood in his way. She is concerned that Darkrai's challenge may be a trap, as he normally flees when confronted, but the group decides to travel to Dark Crater with Cresselia to stop him.
At the bottom of Dark Crater, they confront Darkrai, who further reveals it was also him that caused the player's memory loss and transformation into a Pokémon, by attacking him and Grovyle in the time stream. Despite this, the team prepares to battle Darkrai but he offers them the chance to join him and rule the world. It appears the partner takes it, having given up all hope of defeating Darkrai. However, when the player realizes how uncharacteristic the partner's actions are, they attack Darkrai, revealing it was a nightmare induced by Darkrai. Darkrai summons a group of Pokémon to assist him in eliminating the group but it proves to be useless.
Following their victory over Darkrai and his followers, Cresselia moves in on the defeated Darkrai to finish him off but Darkrai tries to escape through a dimensional hole. Though he is unsure of where, or even when, it will take him, Darkrai is confident that he'll simply be able to complete his plan in another place and time without the group's interference. Right before Darkrai can enter the Dimensional Hole, Palkia arrives to end Darkrai's meddling once and for all. Tired of Darkrai's threats to the fabric of space, Palkia attacks Darkrai moments after he entered the dimensional hole, shattering it in the process.
Darkrai survives this encounter, but, like the player before him, loses his memories and end up somewhere else in the world. As his thoughts and ambitions for world domination were also erased by this, Darkrai is deemed to no longer be a threat and the group leaves him to a fate of wandering aimlessly by himself. He can be encountered and even recruited in several different places after this, similar to other Pokémon players can find in a dungeon. Specifically, he appears in the Mystifying Forest (13F), Lower Crevice Cave (B2F), Miracle Sea (B3F), Mt. Travail (17F), or Spacial Rift (B14F), as long as the player has a Mystery Part or Secret Slab in their bag.
Darkrai is a dangerous and cunning foe, preferring mind games and deception using his nightmare powers to outright battle. He also showed a great deal of planning, even preparing an escape route in the event the group defeated him in the final battle. He appears to be somewhat cowardly, as Cresselia says he normally flees if he's confronted and when finally confronted for the final showdown, he summons his minions to assist him instead of fighting them alone, then attempting to escape through time itself after his defeat. He is evil and has dreams of world domination, not caring if he has to destroy all of space and time if he must, so long as it creates a dark world to rule in the end.
Following the loss of his memory, Darkrai manages to completely reform into a good and noble being with a strong sense of loyalty and commitment to his cause by the time the player finds him again, since his previous personality had also been erased by that event, ultimately giving him a second chance at life.
For more information on this Pokémon's species, see Darkrai.