Vegeta: From being a killer who wants to rule the universe while at the same time wants to eliminate Freeza out of the picture for tormenting him and destroyed his dream where he can be the next King of his home planet.
Android/Cell Arc: This time he has a different goal. He wants to surpass Goku a low class warrior who is superior to him on every way when it comes on battle but he still failed to do so especially that Goku died at the end.
Boo Arc: While Vegeta almost like or love to stay on Earth but still he kept training because that's just his blood and trained his own son as well. But when Goku returned on Earth again and showed how much he progressed and broke the SSjin wall and no matter how much training Vegeta went through and how many years has been passed the gap between him and Goku remains exactly the same. But Goku only got a day to stay on Earth and Vegeta is never gonna get a chance again but with ongoing thing with Boo and he discovered that a Majin boost is the only way for him to equal Goku in just a day so he took a risk and got stronger even though he refused to someone to help him but he was really desperate at that time. Later he admitted that Goku is superior to him during the battle against Majin Boo and he finally understand why Goku will always be one step ahead from him.
Piccolo: The demon himself (or he thought he was) wanted to rule the Earth but with the Saiyans coming on Earth to invade the planet. He decided to team up with the good guys for time being and training his rival's son who possessed a great potential and might saved them from the Saiyans invaders. While training Gohan, he learned how to have a friend and showed him another side of him that he probably would never find it by himself. His friendship with Gohan was the reason he died in the first place even though he knew how much worth his live was because of the DBs and yet he doesn't want Gohan to get killed and let himself got killed instead. While on King Kai's planet he trained (whatever he got stronger) and wants to saved Gohan from Freeza which he pretty much did along with the help of Goku and others. He also admitted that Goku is a great guy but a terrible father.
Gohan: This kid was just a 4 years old and wanted to become a scientist or something but one fateful day when his uncle invade the Earth pretty much changed his entire life. His father died at that day and now he was groomed to be a warrior that will defend the planet even though he doesn't want to but he went along with it anyway. During the fight against the Saiyans, Gohan couldn't just handle the pressure and was scared to death that it took the death of his new friend Piccolo for him to get brave and went on to try fight Nappa and later Vegeta which successfully defeated them along with the help of Goku, Krillin and of course Yajirobe.
With others being dead and Gohan felt that it was his fault that there are no DBs anymore and he wanted to bring Piccolo back to life as well. He decided to step up and wants to find the Namekian DB along with Bulma and Krillin and stands up against Chi Chi as well. He showed a tremendous bravery during the Namek arc against the likes of the Ginyu force and Freeza and let's not forget that Gohan was just a 4-5 years old back then.
While on Cell arc, he finally learned how to be warrior but the minor problem was that how he doesn't really want to kill which isn't part of his character at all but at least he got his moment.
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