Super Saiyan 2
Ever since the start of Dragonball Z, it was implied that Goku's first son Gohan, had the inner potential to become stronger than his father. Even as a little kid, his power already far surpassed that of his dad. Whilst in preparation for the clash at the Cell Games, Goku and Gohan used the Room of Spirit and Time to train. It was during this session that Gohan briefly demonstrated his dormant power. After this occurring, Goku became convinced that not he, but Gohan instead, was the one to defeat Cell.
After Goku threw his battle with Cell, he called upon Gohan to take over. Gohan powered up to his full power, hereby already surpassing his dad. Despite his massive power however, Gohan's kind nature prevented him from defeating Cell. After giving a brief speech about his hidden powers, Cell started torturing Gohan, intent to discover his hidden power for himself. Gohan still refused to fight back however, infuriating Cell. In response, Cell created seven miniature versions of himself, called the Cell Jr's. Witnessing his friends getting killed, and the destruction of Android 16 at the hands of Cell, Gohan snapped with anger, transforming into a Super Saiyan 2. At this stage, Gohan eventually defeated Cell.
Later on in the series, it was revealed that Goku had also gained the Super Saiyan 2 transformation during his seven years' worth of training in Other World. Vegeta most likely also obtained the ability to transform in these years.
A Super Saiyan 2 possesses an amazing amount of power, even several times more than a regular Super Saiyan. As such, the Saiyan can now put enormous amounts of ki into their attacks, potentially turning even the simplest of attacks into deadly blows. Besides the increased power, the Saiyan's speed also increases substantially. Gohan for example, managed to grab a bag of Senzu Beans away from Cell, who at that point in the series, was most likely established as the fastest creature to have ever been featured in the Dragonball universe.
A Super Saiyan features the same basic characteristics as the regular Super Saiyan. The hair undergoes a noticeable change with some characters, become more defined, spiky, and growing sharp ends on top of the strands. Furthermore, the Saiyan now has lightning currents accompanying their aura. Note that the lightning is also visible when the aura is down. Another change is visible in the aura's brightness, though this might be harder to spot at times. In the manga, the shape of the aura itself also undergoes a drastic change. This change however, is not nearly as apparent in the anime adaptation.
 Characters that used this transformation:
Super Saiyan 2 is shown with even spikier hair. The gold aura is surrounded by electricity. The person also maintains a serious face.
 People who have skipped the transformation to SSJ3
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