He didn’t have to deal with a Tamagami boosted up to a new power level, and only needed to reach Super Saiyan 2 to get his victory. Now that Vegeta has broken the ceiling on Super Saiyan 3 use ...
However, he then started training with Whis, and eventually unlocked Super Saiyan Blue. Vegeta and Goku had both acquired God Ki, and their power was absolutely impeccable as the series went on.