It could be a genetic mutation in the fanfic's storyline. Some strange event or factor could have caused a change in Bardock's genes, making it possible for him to become Super Saiyan. This genetic change might be related to some ancient Saiyan lore or a new element introduced in the fanfic's universe.
Well, if Naruto goes Super Saiyan 3 in a fanfiction, he would likely gain an insane amount of power. His physical abilities would skyrocket. He could move at incredible speeds, and his strength might be enough to shatter mountains. His chakra would probably combine with the Saiyan power in some unique way, creating new and powerful jutsu.
Well, in this fanfiction concept, Naruto going Super Saiyan 4 could also lead to some interesting character dynamics. His friends might be initially shocked and a bit scared of this new form. Naruto would then have to prove that he's still the same person despite this radical transformation. And as for the enemies, they would surely be caught off - guard and have to quickly come up with new strategies to deal with this super - powered Naruto.
Vegeta would also be an important character. His rivalry with Goku would intensify even more. Seeing Goku achieve the Super Saiyan form early would fuel his jealousy and his desire to become stronger. He might even try to find new ways to train or gain power to catch up with Goku.
In a Naruto goes Super Saiyan Rose fanfiction, the story could start with Naruto feeling a strange energy within him. This energy could be related to the Super Saiyan Rose form. As he tries to understand it, he discovers that it gives him enhanced speed, strength, and a new set of abilities. He then has to learn to control it while also dealing with the reactions of his friends and the ninja world around him. For example, Sasuke might be initially suspicious of this new power Naruto has acquired.
One common plot is Naruto using his Super Saiyan power to defeat enemies that were previously too strong for him. For instance, Orochimaru might seem like a pushover once Naruto can go Super Saiyan. Another plot is about Naruto trying to hide his new power at first, fearing how others will react. Then, when the situation gets dire, he reveals it and saves the day. It's like a classic superhero - type plot.
The change of Bardock becoming Super Saiyan in the Vegeta fanfic can completely rewrite Saiyan history. It could start a new era of Saiyan pride and power. Bardock, with his new - found Super Saiyan form, might be able to teach the younger Saiyans about the transformation. This could lead to a more united Saiyan race, as they all work towards achieving the Super Saiyan state. It might also mean that they are not as easily defeated by Frieza, as they have a stronger force to oppose him. This could result in a different galactic power structure, with the Saiyans being a more dominant force.