In a way, Maul's mission during the final days of the Clone Wars was to stop Darth Sidious' rise to power. To do that, Maul planned to ambush Anakin Skywalker on Mandalore during the siege of the planet and kill the Jedi who would become Palpatine's new Sith apprentice and ultimate weapon.
Maul did intend to draw Obi-Wan to Mandalore and he counted on Anakin Skywalker coming as well. Through his vision of the future, Maul realized Anakin was the key to Palpatine's plans. He intended to kill Anakin on Mandalore, thus throwing a major wrench in Palpatine's schemes.
At the end of the Clone Wars, Maul had a vision of Anakin Skywalker's fall to the dark side and transformation into the Sith apprentice of Darth Sidious.
The Phantom Menace
In his first appearance, Darth Maul is sent by his master Darth Sidious (Ian McDiarmid) to capture Queen Padmé Amidala (Natalie Portman) of Naboo to force her to sign a treaty that would legitimize the Trade Federation's invasion of the planet.
However, Maul's hatred of the Jedi was more personal. He was filled with anger when he realized that as a child, the Jedi had not come for him. Maul did not know if they found him unworthy or simply ignored him, and their neglect fueled his rage, counting the days until he could have his revenge.
Darth Maul feared Vader in the same way as anyone would. Vader was the most notorious and ruthless figure in the Empire, using his rage and anguish to fuel his resolve, enabling him to dispatch his enemies without compassion or remorse.
Darth Maul died during a final battle with Obi-Wan in the Rebels TV series, and Palpatine couldn't have cared less. For him, finding and killing Maul for his failure simply wasn't worth the effort.
"Is it the Chosen One?" Maul asked. "He is," Kenobi replied. Maul looked up, the life fading from his eyes, and uttered his last words. "He will avenge us."
Even in the old Star Wars canon, the two had a confrontation, as they met in the comic book Star Wars Tales #9, where Maul pieced together that Anakin was Vader.
Like his master, Darth Sidious, better known as Sheev Palpatine, Maul's main weakness was his overconfidence. In Luke Skywalker's confrontation with Palpatine during The Return of the Jedi, he tells the Emperor that his overconfidence is his weakness.
Always a canny foe, Ventress baited Anakin by threatening to kill Padme Amidala, before striking him across the face. The scar became another symbol of Anakin's journey to the dark side when he punishes Ventress by binding her in cables and flinging her from the top of a skyscraper.
Rivalry: Obi-Wan Kenobi
There is absolutely no question that Maul's greatest rival is Obi-Wan Kenobi. Not only is he the man who presumably killed Maul on Naboo, but he is the man for whom Maul had such deep hatred and anger for that it kept him alive.
Anakin Skywalker was the Chosen One, conceived by the Force itself. According to Star Wars: Episode I - The Phantom Menace, he had a midichlorian count higher than even Master Yoda. This meant he had the potential to access the Force and achieve feats no other Jedi or Sith had ever managed.
Intimacy Level. Maul once tried to turn Ahsoka to the Dark Side, but failed. Maul calls her "Lady Tano" to mock her.
Darth Maul and Obi-Wan's long-standing rivalry started in Episode 1 and lasted all the way until Star Wars: Rebels. Throughout his lifetime, Maul seemed to hate Kenobi! Every time Maul says Kenobi.
By the time of Episode 3; Anakin is in his prime, and already one of the Jedi Order's most powerful “masters” (although technically still a knight), just behind Obi-Wan, Windu, and Yoda. Maul wouldn't stand a chance. Anakin stomps.
In many ways, Palpatine enslaved Vader and, over the years, Vader undoubtedly grew to resent his master. Because with any Sith duo, the relationship is always one of master and servant. And due to the history of the Sith, both these Dark Lords were probably constantly paranoid about being betrayed by one another.
The duel. Darth Vader defeats Darth Maul. The two Sith Lords engaged in a lightsaber duel, going through the volcano and onto a bridge situated over a river of lava, which collapsed, though they both survived and continued their battle.
In the end, Darth Vader's inner hatred and darkness made him the winner of the epic battle against Darth Maul.
Vader was far more powerful than Maul or Dooku ever were, and Maul realised he had been used. Vader was always destined to replace him, and Palpatine was merely using him as a placeholder.
Obi-Wan Kenobi, during his confrontation with Vader on Mustafar, stated that he believed Anakin was indeed the Chosen One, but that his destiny had been altered, and the prophecy left unfulfilled. Anakin fulfills the prophecy by killing Palpatine. Skywalker's sacrifice brings balance and redemption.
DARK SIDE FRIDAY - Did you know Palpatine feared Qui-Gon Jinn? Palpatine was immensely powerful and he could see the future which made him very confident about pretty much anyone who stood against him. So why Qui-Gon Jinn?
After learning that Palpatine was secretly the Sith Lord Darth Sidious, Dooku turned to the dark side and became a Dark Lord of the Sith himself, replacing Darth Maul as Sidious's second apprentice. His new master bestowed upon him the Sith title of Darth Tyranus.
In the novel, Dooku remains silent when Sidious tells Anakin to kill him, because he finally realised, that he had been replaced. His master has found a new apprentice, younger, filled with more rawness and power to destroy the Jedi.