In the Star Wars universe, redemption for villains usually goes hand in hand with another thing: death. In The Rise of Skywalker, that pattern holds true, with Kylo Ren finally finding his way back to the Light Side, only to meet his doom soon after. So how does Kylo Ren die? That's actually a more complicated question than it might seem.
Officially, Kylo makes it all the way to the end of the movie, when he joins Rey to try to defeat the resurrected Emperor Palpatine. Their Force bond is co-opted by Palpatine, who sucks all the power from it to rejuvenate himself and his powers before tossing an unconscious Kylo into a ravine. Rey is forced to defeat Palpatine on her own, using the lightsabers of Luke and Leia to turn his own Force lightning on him, but the energy required costs her her life. Kylo climbs out of the ravine, finds her body, and, in a reversal of an earlier scene in which she heals him, revives her with the Force — which almost immediately kills him.
Depending on how you interpret the dichotomy between Kylo and Ben Solo, however, it's arguable that "Kylo Ren" dies long before this. The idea that a fallen Jedi's Dark identity kills their heroic side is one that dates back to the original trilogy, when Obi-Wan Kenobi tells Luke that Darth Vader "betrayed and murdered" Anakin Skywalker. Based on that interpretation, Kylo dies earlier in the movie, when he hears his mother's voice calling to him through the Force then sees a memory or Force projection of his father reassuring him that Ben Solo is still alive. However you interpret it, Kylo definitively dies in the movie, as does Ben Solo. In a way, it's a fitting end: much of his arc is tied up in trying to imitate his grandfather, and in the end, he does, but by embracing Anakin's legacy, not Vader's.