Legendary Super Saiyan
Legendary Super Saiyan is a Toei Animation variant on Akira Toriyama's original Super Saiyan legend, as introduced in the Dragonball Manga. Because this transformation is originally created by Toei, it is regarded as non canon. This transformation appears twice, in the eigth Dragonball Z movie, Broly: The Legendary Super Saiyan, and in the tenth movie: Broly: Second Coming. It was only achieved by a Saiyan called Broly, another survivor of Planet Vegeta's destruction.
Broly was made out to be the "true LSSJ" because Akira Toriyama revealed more Super Saiyans in the manga after Goku when he originally planned to end the series after the Frieza Saga. They created Broly as an explanation for that to show what the LSSJ was really supposed to be - a mysterious warrior possessing omnipotent strength that was destined to be unlocked, standing out from the rest in his race. This is what he was iconic for and had an untimely death. What also made him Legendary was his insatiable lust for bloodshed and causing an "unstoppable" path of destruction, untempered by any emotion other than hatred. Broly is the apocalypse for wiping out nearly the entire south galaxy, and would've gone for the north one had Goku and the others not tracked him down and put a stop to it. Paragus said he wouldn't of stopped until they reached their new home world.
Broly's LSSJ state is a stepping stone to his ultimate power. This puts his status above the normal SSJ's who don't share any of his unique traits, thus fulfilling the regular Super Saiyan Legend that Vegeta referred to. Broly became the first SSJ since the original so by including non canon material, he deserves the credit for both Legends. Everything here sets him apart which is why in the movie, he says "You're all complete and utter wastes of Saiyan blood!" To put this matter in simpler terms: The legend of becoming a Super Saiyan is different than the actual Legendary Super Saiyan who most people believe Broly to be, including Funimation for all the reasons stated.
This transformation in terms of appearance, seems to mimic the second grade of Ascended Super Saiyan, that in the canon of Dragonball was shown by Future Trunks and Goku. One big difference between these forms is that although both massively increase the user's power level, the Legendary Super Saiyan form only seems to gain speed instead of losing it, which was the main drawback about the Ascended Super Saiyan form. Another noteworthy aspect is that Broly's power is stated to constantly grow in this state, also making it unique amongst other Super Saiyan forms that gradually grow weaker during battle, as the user's ki level steadily decreases.
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