Super Saiyan 2
From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Super Saiyan 2 (超サイヤ人 二, Chō-Saiya-jin Ni) is the direct successor to the first Super Saiyan transformation. It is very similar to the original form in appearance and attainment, however, the power output is far greater, as speed, strength, and energy output all drastically increase. Son Gohan is the first person to attain the form when he fights against Cell in the Cell Games.
The golden hair brought on by the original transformation becomes longer and rigid; any hair that hung loose in the Super Saiyan transformation (in the case of Goku or Gohan, because Vegeta lacks any bangs in front of his face, as does Gotenks) is now raised. Increased energy radiation causes the aura to take on a jagged, fierce flame-like appearance rather than smooth or flowing. Because the energy output and radiation is higher than that of any Super Saiyan, the aura pulses at a higher frequency, like the type 2 aura, at least in the manga. Muscle mass is barely increased, but energy output is multiplied manyfold; such that greater amounts of the Saiyan's increased energy capacity can be used at once for much more powerful energy attacks, and even speed is augmented incredibly by the boost, unlike the Ascended and Ultra Super Saiyan states which cause the muscle mass to swell and thus impede the user. Another notable feature of the form featured in almost all Dragon Ball Z games and some scenes of the show as well as pictures from the manga, is the electrical aura, many electrical sparks (normally blue, gold in Dragon Ball Z: Budokai 3) that constantly surround the body — especially when charging up. However, they aren't always present (especially in the anime; Gohan and Vegeta aren't the only ones who lack the trait completely in some episodes), and some fans sometimes mistake a charging Super Saiyan for a Super Saiyan 2 due to the lightning sparks, such as Vegito; in the manga, they never reappear in his aura after his transformation, nor are they ever shown on any other first-level Super Saiyan. 
In order to achieve this transformation, the Saiyan must first gain a huge amount of energy (usually by training), far beyond that required for the first Super Saiyan form. Once enough energy is acquired, the Saiyan must experience a powerful emotional upheaval, much like the Super Saiyan transformation, but to a greater extent. Because of the intense emotion required to initiate the transformation, any mastery of the Full-Power Super Saiyan state, and mental stability attained therein, is negated, and the naturally remorseless nature of the Saiyan race is magnified, requiring them to remaster the personality changes. Even the gentle, polite Gohan becomes a hotheaded, merciless fighter after transforming, opting to torture Cell rather than kill him despite Goku's pleas. The power output emitted by this form is greatly increased as well, as it doubles the strength of the regular Super Saiyan transformation, as stated by the Super Perfect Guide. 
Usage and power
The Super Saiyan 2 form was chronologically achieved by Gohan after witnessing the Cell Juniors' attack on the Z Fighters and Android 16's death at the hands of Perfect Cell. The power of the Super Saiyan 2 form skyrockets far beyond the power of the Super Saiyan, Ascended Super Saiyan, Ultra Super Saiyan, and even Full-Power Super Saiyan forms. Perfect Cell and Bojack, who could both easily dominate those in the Ascended and Ultra Super Saiyan forms and were somewhat stronger than Full-Powered Super Saiyans even without accessing their full strength, were easily slaughtered by Gohan in his Super Saiyan 2 form. In addition, when Perfect Cell produced seven Cell Jrs, each of the Z Fighters were unable to fight evenly with even one of them (including Goku, Vegeta and Future Trunks, but the former was exhausted from his previous fight with Perfect Cell himself). However, when Gohan fought the Cell Juniors in his Super Saiyan 2 form, he killed all of them effortlessly on his own in simple, single blows, and was unaffected by their most powerful attacks.
Gohan proceeded to fight and severely injure Perfect Cell with just two punches, even after the android unleashed his full power. However, in a Kamehameha struggle against Super Perfect Cell, Gohan had a very hard time due to having his left arm broken by Super Perfect Cell's attack when he defended Vegeta after he attacked the Android to try to avenge his son's death (a blast which was stated to reduce Gohan's power output to less than half its normal amount). It was only a little help from Goku and Vegeta that Gohan needed to summon enough power to destroy Super Perfect Cell.
Seven years after the Cell Games, Gohan demonstrated the Super Saiyan 2 transformation to Kibito at the World Martial Arts Tournament. The Daizenshuu also states that Gohan also used his Super Saiyan 2 form during his battle against Dabura. However, Vegeta mentioned that Gohan's Super Saiyan 2 form was now much weaker than when he fought Perfect Cell due to his lack of training.
Following the events leading up to Majin Buu's revival, Goku and Vegeta (after becoming a Majin by Babidi's spell) fought evenly matched in their Super Saiyan 2 states. The power of Majin Buu is shown to far surpass the power of the Super Saiyan 2 form; Vegeta inflicted little damage to the monster, and even after he expelled all of his energy at once in a devastating suicidal explosion, Majin Buu managed to fully regenerate after some time.
When Vegeta returned to Planet Earth from the Next World (with the help of Uranai Baba), he and Goku fought Super Buu in their Super Saiyan 2 forms. However, due to the massive power he achieved from absorbing Gotenks, Piccolo, and Gohan, Super Boo's strength easily outclassed Goku and Vegeta, reverting them back to their normal states. It was not until Goku finally convinced Vegeta for both of them to wear the Potara Earrings so they could fuse into Vegito, giving them enough strength to easily dominate Super Boo.
During the fight with Kid Buu on the Sacred Kai Planet, Goku and Vegeta battled as Super Saiyan 2's for a short time (in the anime only, because Goku went straight to Super Saiyan 3 in the manga, stating that he would have no chance if he did not use his full strength). However, Goku ended up transforming to the Super Saiyan 3 level.
It is stated in Dragon Ball: Daizenshū 7 that Gotenks can theoretically transform into Super Saiyan 2. However, due to bypassing Super Saiyan 2 when transforming from a Super Saiyan into Super Saiyan 3, his complete Super Saiyan 2 form is never fully revealed, and remains unused.
Furthermore, during Dragon Ball GT, Gohan and Vegeta used the Super Saiyan 2 form from time to time during battle. However, by this time, it had been majorly outclassed by Super Saiyan 3 and the new Super Saiyan level, Super Saiyan 4. One strong case for Gohan and Vegeta's usage of the Super Saiyan 2 state is when they, along with Goten, Trunks, and Majuub, power up to fight Super 17. Here, the robust aura associated with the Super Saiyan 2 state appears on Gohan and Vegeta, but not on Goten or Trunks, both of whom never assumed the state; the lightning sparks, however, are not present. When Goku appears on the battle field, he fights Super 17 in the first level Super Saiyan state before using the Super Saiyan 4 form without any usage of either the Super Saiyan 2 or Super Saiyan 3 levels.
The Super Saiyan 2 form made its first movie appearance in the film Bojack Unbound, where the Z Fighters were struggling to combat Bojack and his henchmen. After being saved from Bojack by Goku (who used Instant Transmission to teleport to Planet Earth) and hearing his father's words of encouragement, Gohan tapped into his Super Saiyan 2 powers and defeated Bojack and his henchmen in a matter of minutes.
Gohan also used this form to battle Broly when the latter reappeared in Broly: Second Coming, and despite putting up a far better fight than he did previously, he was outstripped by the Legendary Super Saiyan's massive power. However, this was partially because of Gohan's lack of training that made him noticeably weaker up to that point, and since Broly survived being punched in the stomach by Goku in Broly: The Legendary Super Saiyan, Broly's power most likely increased substantially after recovering from near-death (as all Saiyans do). Though, to Gohan's credit, his blows managed to inflict a noticeable level of injury to Broly (whereas nobody in Broly's first appearance could damage him in the least), as Broly was knocked back when he was kneed in the face by Super Saiyan 2 Gohan.
The Super Saiyan 2 form was also used in Fusion Reborn and Wrath of the Dragon against Janemba and Hirudegarn, respectively. In both of the films, however, either fusing or the Super Saiyan 3 form is used to kill the main enemy.
- Gohan is the first to achieve the Super Saiyan 2 form, with Goku and Vegeta following suit. Goku learns it in Other World and Vegeta learns it through intense training.
- When Gotenks (the fusion of Trunks Brief and Son Goten) transforms directly to Super Saiyan 3 from Super Saiyan (the first form), they seem to skip Super Saiyan 2.
- In Dragon Ball Z: Budokai 3 and in Dragon Ball Z: Infinite World, Future Trunks was given the form Super Saiyan 2 even though he had never taken that form in the series. Ending up virtually no different to his previous form in the game in terms of looks and techniques. It became clear that it was a mistake made by the game developer that remained in the game since Dragon Ball Z: Budokai 2 contradicting Trunks having the correct form of Ultra Super Saiyan in the first game of the Budokai series.
- In Dragon Ball Z: The Legacy of Goku II, this form is incorrectly named Super Saiyan Rage. This was, however, fixed in its sequel in which Gohan states it to be a form "far beyond that of Super Saiyan" and Goku labels it "what you could call a Super Saiyan 2". It is, however, not playable in a different fashion like in the previous game, whereas Super Saiyan 3 is. This was stated to be so because it looks so similar to the original form in the anime that it is almost difficult to distinguish it from its predecessor.
- In Dragon Ball Z: Budokai Tenkaichi 3, Goku (GT) has all his Super Saiyan transformations with the exception of the Super Saiyan 2 form (although unlike Gotenks, Goku does transform into the state in the series). Also, in Infinite World, Goku and Vegeta's GT versions have all their Super Saiyan transformations apart from Super Saiyan 2.
- This form is the only form never to have been taken by a fused entity, as all three Saiyan fusions have used the first transformation, and Gotenks and Gogeta use the third and fourth forms respectively. However, Gotenks very much could take the Super Saiyan 2 form.
- The Super Saiyan 2 form is twice as strong as a regular Super Saiyan, according to the Dragon Ball Super Exciting Guide: Story Volume, pages 62-63.
- In the FUNimation dub of "Super Saiyan 3?!", Goku states that Super Saiyan 2 is also known as Ascended Saiyan. This should NOT be confused with the Ascended Super Saiyan, however, which is a branch of the Super Saiyan level.
- According to Goku's flashback, Gohan technically first transformed into this form during their training in the Hyperbolic Time Chamber, though he was too exhausted to maintain it. This is the reason why Goku knew about this power before Gohan transformed into it during his fight with Cell.