The 2nd arc of DBZ begins with the Garlic Jr. Saga and during this time, Vegeta is scouring the cosmos for any sign of Goku. Vegeta’s proud mentality will not and cannot allow a sub-class Saiyan to exceed him in strength and power. Vegeta covets the new power that Kakarot has achieved and wishes to taste the power for himself. What drives him so obsessively to find Goku is that Goku refused to return home from space when his friends learned he survived Namek’s explosion and tried to wish him back to Earth. Vegeta thinks that Goku is out training and honing his Super Saiyan abiities and Vegeta cannot let himself be idle. He must be the strongest warrior at all times.

Returning to Earth unsuccessful, Vegeta senses that Frieza survived and is headed towards Earth and heads to the desert with the other Z fighters to confront him. Vegeta is determined to show Frieza that he’s improved and to beat him this time. It should be noted that Vegeta at this period in time no longer has any bad blood or settles to score with any of the Z fighters. After Frieza’s ‘defeat’ at the hands of Goku and being wished to Earth, Vegeta abandoned his crusade for immortality and power and seeking planets to destroy. Clearly, as Vegeta had admitted to Goku, all that was because of what Frieza made him. He no longer has an interest or desire for conquest and has settled for a life on Earth. However, he becomes mingled with the Z Warriors because of Bulma’s friendship to them and Vegeta’s place of residence is Capsule Corp where Bulma lives. Why he never left is anyone’s guess seeing as how he’s admitted that he needs nobody’s help and sees the Z fighters as inferior. Perhaps it is the hospitability of the Briefs family which acts as an incentive for him to stay. A mysterious youth appears and handles Frieza and his father King Cold without breaking a sweat which surprises Vegeta but what surprises him even more is that the youth can transform into a Super Saiyan just like Goku. When the youth (Trunks) tells him that he is a Saiyan, Vegeta calls him a liar since the only known Saiyans to exist now are himself, Gohan, and Goku. After Goku arrives, Goku shows off his incredible Super Saiyan power as well as the new Instant Transmission technique and to make matters worse there are now 2 Super Saiyans and Vegeta is not one of them. Vegeta is beginning to feel himself being left in the dust as Goku continues to learn new abilities while Vegeta feels he hasn’t progressed at all.

Trunks tells the Z Warriors about the coming of 2 Androids in 3 years. Always ready to prove himself for a fight, Vegeta accepts this new challenge and chooses to fight alongside the Z fighters. He accepts if only just to prove his power and not for the sake of the planet or the Z fighters. They are not his enemy anymore but Goku still is which is why he tells him that once the Androids are dealt with, he will deal with Goku to settle their score. It is not clear how Goku perceives Vegeta at this moment but what is obvious is that he doesn’t see him as threat. After working together on Namek, Goku no longer sees Vegeta as an enemy. Goku may not even know that Vegeta harbors a secret hatred for him and when he agrees to settling the score with Vegeta, I think that Goku may think that it is a match simply to prove who is the stronger fighter, not a battle to the death which Vegeta may have in mind. Perhaps it simply is meant to be an exhibition match but Vegeta’s motives are unclear. For 3 years, the Z Warriors train and Vegeta uses the gravity technology inside one of Dr. Briefs’ Capsule Corps spaceships to push himself to his limits determined to be the very best again and strongest like no one ever was.

3 years pass and the Z Warriors are facing off against Android 19 and Android 20 aka Dr. Gero. Everyone is there except Vegeta of which Goku points out that he’ll show up because he’d never miss a fight. Vegeta must’ve felt like making a very dramatic entrance because that’s what he certainly did unless he just happened to be late to the party but knowing that the Androids were going to be there, we’ll go with the former. As Goku begins suffering from the heart virus that Trunks warned about and 19 prepares to finish him off, Vegeta steps in and stops him from taking Goku’s life because destiny has reserved that pleasure for him (https://www.youtube.com/watch?v=niUeoROcNEg). Telling Goku he’s next after he deals with the Androids, Vegeta surprised everyone by transforming into a Super Saiyan. Gohan even questions if he’s still on their side, proving that none of them really know where his loyalties lie and also questions that he thought a Saiyan had to be pure-hearted to become a Super Saiyan to which Vegeta answers that a Saiyan needs a motivation based on rage which in this case for him was closing the gap between his and Goku’s strength level. For Goku that rage and motivation was the loss of Krillin and avenging his death and for Trunks it was ditto for his mentor Gohan. Now possibly stronger than Goku as Goku goes home to take the antidote given to him by Trunks and rest, Vegeta disposes of 19 and prepares to take on Gero who flees. In typical Vegeta fashion, he disregards the rest of the Z fighters and takes off to deal with every forthcoming threat on his own now that he’s a big bad Super Saiyan. This affects and influences him so much that he thinks he’s beyond accepting help from anybody and that anyone who is not him is inferior, that he is the absolute strongest there is, as well as thinking that he’s invincible.

This blind arrogance gets him into quite some hot water after he follows Gero into the northern mountains where Gero plans to release Androids 17 and 18. Trunks tells the Z fighters they must get there before Gero at all costs to destroy the Androids but are too late. After the Z fighters gather around Gero’s hidden base, Vegeta blasts the lab doors open to see the Androids have already been activated. When the Androids leave to complete their programming (Android 16 included) to find and kill Goku, Vegeta thinks they leave out of cowardice. He hunts them down and challenges them all at the same time but only 18 steps up to fight him. Immediately thinking misogynistically, Vegeta promises to take it easy on her, not knowing what she has in store for him which is one of his most humiliating beat-ups ever. Toying with him, 18 literally drags Vegeta’s pride into the dirt and leaves it there after breaking his arm, leaving him screaming. Reeling with anger that she made him bleed after he regains consciousness, he storms off prompting Trunks to follow him but Trunks is stopped by Piccolo, knowing that Vegeta wants to be alone because his pride was shattered.

The next we see Vegeta, he’s been standing on a cliff edge for 3 days introspecting and pondering on if there’s a way to surpass Super Saiyan. The last battle with 18 has given him some clarity that he’s not as strong as he thought and must ascend to the next level. Goku, who had been sensing everything that’s been going on and sensing Vegeta’s new aspirations while in rest, approaches him about receiving one year’s worth of training in one day in the Hyperbolic Time Chamber on Kami’s Lookout. At this point, Imperfect Cell has already attacked and absorbed many people from various cities while Piccolo has fused with Kami and is on Cell’s trail with Tien and Krillin. Once again, Vegeta’s primary interest in this is only to improve his abilities; Cell will be just another perfect target for him to practice his new strength on once he obtains it. Goku, Gohan, Vegeta, and Trunks go to the Lookout and enter in pairs with Vegeta pairing up with Trunks. Trunks, for those who do not know, is Vegeta’s son from the future. Vegeta came to this realization when Trunks came to their timeline a 2nd time and figured his name was the same as the child he bore with Bulma in the 3 years. Vegeta takes his training so seriously that he forbids Trunks from talking about it to anyone and especially to Goku, probably not wanting him to know exactly what he did to ascend. With mighty hubris and belittlement towards Goku, Vegeta again chooses to deal with the threat himself and goes down below to confront Cell as Trunks follows him.

At this point, Cell is in his 2nd form after absorbing Android 17. Vegeta introduces himself to him and wastes no time with formalities. Upgrading to Super Saiyan Second Grade (not Super Saiyan 2), Vegeta lays a flawless beatdown on Cell and could have easily finished him off. Thanks to his Saiyan nature magnified by his own personality, Vegeta wants the thrill and excitement of battling a worthy opponent and so allows Semi-Perfect Cell to absorb Android 18. This comes back to bite Vegeta as Perfect Cell deals with him swiftly and almost puts an end to his life save Trunks’ intervention who ascends to Super Saiyan Third Grade. The upgrade is too bulky and sacrifices speed which Cell points out that Trunks could surely beat him at his base power level but Cell is too fast and Trunks would never catch him. Cell points out that Vegeta knew this which is why he never upgraded to Level 3. After an unconscious Vegeta wakes, he returns to the Lookout to train more for a rematch against Cell in the Cell Games. Goku tells Vegeta that going back into the Time Chamber is pointless and would only be torture for the body but since keeping up with Goku’s strength is important to Vegeta, Goku tells him to knock himself out. Scoffing that Kakarot would even entertain such a notion as being stronger than him, Vegeta says ‘You make it sound as if you’ve become a great deal stronger than I am’ to which Goku responds ‘Sure. I’m far above you’. As you can imagine this doesn’t sit well with Vegeta and curses Goku for surpassing him a 3rd time (https://www.youtube.com/watch?v=qbhtTlJYy3U). It is possible that Goku has a natural spring of ability beyond Vegeta’s because of the special training he received from Master Roshi, Mr. Popo, and Korin, prior to Vegeta’s arrival on Earth. Not to mention extra training Goku received under King Kai, the training on the way to Namek, and training on Yardrat. Having masters would give Goku an advantage on honing his skills and abilities whereas the only teacher I assume Vegeta ever had was King Vegeta. Plus the Super God Water which unlocked Goku’s potential. If Vegeta had drank the water, who’s to say he wouldn’t be even more powerful than Goku and one step ahead of him. This impressive power is showcased when Goku demonstrates his new abilities, which by staying in Super Saiyan form and making it their natural form, don’t siphon much energy and can still draw out and power up from reserve energy. Overwhelmed by Goku’s new powers and not wanting to become second fiddle, Vegeta enters the time chamber again (https://www.youtube.com/watch?v=CJ-CTHUYN7M&t=86s).

When the Cell Games begin, Vegeta is the first to arrive at the arena and is none too pleased when the other Z Fighters arrive. Vegeta doesn’t argue when Goku volunteers to fight Cell first, to see and observe Goku’s full power. Vegeta is taken aback and astounded when Goku goes to full power who’s a league above Vegeta but not in Cell’s league. Vegeta is even taken more aback when Goku surrenders to Cell and volunteers Gohan for how can a child hope to stand against the powerhouse that is Cell? Vegeta is disgusted that he struggles against one of the Cell Jrs but manages to hold his own. He witnesses Gohan transform into Super Saiyan 2 and Goku sacrifice his life when Cell prepares to blow himself and the planet up but Vegeta’s first conversion moment happens when Cell strikes Trunks with a Death Beam after returning to life. Realizing how much Trunks actually meant to him and how he’s only ignored him all this time, Vegeta flies in a rage and attacks Cell albeit in vain as Vegeta is swatted like a fly to the ground. After Gohan stops an attack from Cell that was meant for Vegeta and mangles his arm, Vegeta apologizes to Gohan because he feels useless and also because he feels the situation is unwinnable and hopeless (https://www.youtube.com/watch?v=cYFgxsaVddg), (https://www.youtube.com/watch?v=wrZh4Mk5jGk). Vegeta has never apologized to anyone in his life and Gohan is bewildered and confused to this deviant course in Vegeta’s personality. Gohan is then caught in a Kamehameha power struggle that, were it not for an assist blast from Vegeta, he might’ve lost (https://www.youtube.com/watch?v=qVtK6dx_DLY).

After the battle is won, Vegeta introspects again and beats himself up for being half the Saiyan Goku ever was. Goku made the sacrifice play for his friends and gained a victory through his son. Vegeta feels completely beaten. Nothing he can do now will ever measure up to Kakarot. Vegeta considers himself a warrior no more and vows to stop fighting plus he’ll never have the chance to prove himself against him which is everything he’d been working towards (https://www.youtube.com/watch?v=GJ64JXN_3mI). At the end of the Cell Arc, Vegeta sees Trunks go back to his time and says goodbye, their relationship improved after how Vegeta reacted to his son’s fatal blow.