There are few beings in the Dragon Ball mythos more powerful than a Legendary Super Saiyan, though Dragon Ball Super revealed the one way to take them down–a method that is greatly effective in more ways than one.
A Legendary Super Saiyan is an extremely powerful and incredibly rare Super Saiyan form that only manifests in a Saiyan every one thousand years. Once the Saiyan in question undergoes the transformation into Legendary Super Saiyan, they enter a kind of berserker state in which they have little to no control over their actions. While in this state, the Legendary Super Saiyan is seemingly tapped into an unlimited supply of energy, making them practically invincible.
In Dragon Ball Super Chapter 38 by Akira Toriyama and Toyotarou, Goku, Vegeta, and the rest of the Z Fighters encounter their first Legendary Super Saiyan during the Tournament of Power, a Saiyan from Universe 6 named Kale. Going into the tournament, Kale and her fellow teammates didn’t know she was a Legendary Super Saiyan, though every participant quickly learned that’s exactly what she was after she made the transformation and single-handedly eliminated nearly half of the fighters in the arena. While that seemed like a good thing for Universe 6, one of the tournament rules was that no killing was allowed, and it was only a matter of time before Kale’s power grew too great to contain and she would accidentally kill someone during her berserker rampage. In order to stop Kale without eliminating her from the competition, her teammate, Caulifla, used her Supreme Kai’s Potara Earrings to fuse with Kale so that Caulifla could take control over her mind without losing too much of Kale’s muscle.
While Kale might have been the first Legendary Super Saiyan Goku and Vegeta ever faced, it certainly wasn’t their last. In the anime film Dragon Ball Super: Broly, Vegeta and Goku meet Broly for the first time in the newly established Dragon Ball canon. Broly, as many fans know from his previous, non-canonical appearances, is a Legendary Super Saiyan just like Kale, and the film shows his raw power is enough to match that of both Goku and Vegeta, who have each unlocked god-tier transformations. While separately they weren’t able to defeat Broly, they eventually beat him to the brink of death after they fused together to become the amalgam entity Gogeta, at which point Broly didn’t stand a chance.
In both instances dealing with a Legendary Super Saiyan, fusions were the only way to defeat them. Caulifla stopped Kale by fusing with her to effectively take control of her body and bring her rampage to an end while Goku and Vegeta fused together to out-muscle Broly in truly brutal fashion. Dragon Ball Super confirms the one way to beat a Legendary Super Saiyan, is through fusions.