As the Third Sister, she was highly ambitious. Thus, her mind was set on tracking down Jedi Master
Reva played on Obi-Wan's affection for his Padawan by telling him that Anakin was alive. Even her apparent quest for the role of Grand Inquisitor (which led to her seemingly killing the previous holder of the title) and to antagonize her fellow Inquisitors was all an effort to get closer to Vader.
While she hates Obi-Wan for failing to stop his apprentice from destroying the Jedi Order, Vader himself is the true target of Reva's wrath. She became an Inquisitor in the hope of getting close enough to Vader to kill him, though that doesn't seem to have worked out for her.
The reason that Reva wants Obi-Wan is likely because she was a Jedi present during Order 66. In fact, she may have been one of the young children present in the opening scene during the massacre at the Jedi temple.
The Third Sister Was a Jedi Youngling
The reason why the Third Sister hates Obi-Wan Kenobi so much is because she was a Jedi initiate when Order 66 happened. On that infamous day, Reva was training with her fellow Jedi younglings in the Jedi Temple of Coruscant.
Reva knows that Anakin Skywalker is Darth Vader because she was one of his targets—a child—during the Order 66 killings that took place during the events of Star Wars Episode III: Revenge of the Sith.
Turning to the dark
Sevander eventually escaped the Jedi Temple and turned to the dark side. Wanting revenge on Vader, currently acting as the commander-in-chief of the Galactic Empire's forces, she joined the regime's Inquisitorius as an Inquisitor, in order to get close to him.
Background. Reva was a Jedi youngling who was present in the Jedi Temple during Order 66. When the clones raided the temple, Reva and her fellow younglings found Anakin Skywalker and asked him for help, only for him to kill them all. Reva survived by playing dead, and she swore revenge on Anakin.
The tragic past of Reva, a.k.a. the Third Sister, is revealed in the fifth episode of the Obi-Wan Kenobi series, which Darth Vader is somehow already aware of.
As the Grand Inquisitor made clear, neither he nor Vader had any further use for Reva, and therefore they didn't consider her even worth killing. Instead, they left her crawling in the dirt because, as he had told her before, she was “the least” of them.
Warning!
Kenobi managed to convince Riva to betray her master, Darth Vader, by encouraging her to backstab him. Of course, such a paltry attempt to kill the fearsome villain proved futile – Vader disarmed Reva and stabbed her in the chest with her own lightsaber.
After making an issue of it, Obi-Wan put two and two together and figured out that Reva was a Youngling who survived the massacre at the Jedi Temple perpetrated by Anakin during Star Wars: Episode III – Revenge of the Sith. Reva then confirmed Obi-Wan's assertions and admitted to her plans to betray Darth Vader.
Midway through Episode Five, Reva tells Obi-Wan that she essentially dedicated her life to hunting down and defeating Darth Vader/Skywalker, delivering revenge on behalf of her friends. So Reva has technically been good all along, posing as an Inquisitor to get close to Vader.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
Reva and the other younglings were eventually cornered in the Jedi High Council chamber by the newly-christened Darth Vader and the clones. As the massacre began, Vader stabbed Reva and left her for dead. According to Obi-Wan Kenobi, Reva used the dark side to keep herself alive.
'Obi-Wan Kenobi' Movie Screenwriter Created Reva; Plan Was to Have Darth Vader Kill Her.
Reva was herself skewered by Anakin's lightsaber. But the blow was not lethal—it is said that she drew upon the dark side to keep herself from dying. She also successfully feigned death to avoid further brutality. This enabled Reva to survive the Great Jedi Purge, but the course of her life had unalterably changed.
While Anakin notoriously killed younglings in Revenge of the Sith, perhaps his first steps in embracing the dark side saw him extending mercy where he couldn't bring himself to kill them all, choosing to spare Reva instead.
The duel between the two dark siders also highlighted a few important facts. First off, the fight proved that none of the Inquisitors are very powerful. Reva gave it her all, but she was nowhere near a match for Darth Vader.
Moses Ingram, the actor who played the Third Sister, received the lightsaber as a gift from Lucasfilm president Kathleen Kennedy. The weapon was customized to fit Ingram's hands. Ingram spent a lot of time icing her hands before she learned how to wield her lightsaber.
Former Imperial Inquisitor Reva (Moses Ingram) was left for dead by Vader after she tried to strike the Sith Lord down.
Reva is Mace Windu's daughter who blames Kenobi for his death.
And since the series takes place 10 years after Revenge of the Sith, it can be assumed Reva is anywhere between 18 and 21 now.
Fortunately, he never actually saw her in action - which meant, notably, he never saw Reva trigger her lightsaber. Had he done so, it would have been a major continuity problem, because Luke clearly had no idea what a lightsaber was in the first Star Wars film.
Reva's new mission is to kill a young boy because she wants “justice.” But the only reason she can't kill Luke is because she sees herself in that position. And then, by the end, Obi-Wan lets her live.