Vegeta can mess with Cui soon after you first take control of him in Dragon Ball Z: Kakarot, but there really isn't much to worry about with this fight. His first challenge doesn't come until a bit later after Gohan and Krillin confront Dodoria, with them failing to defeat Dodoria and merely managing to hold him off. Vegeta enters the fight ready to kill immediately and this guide is going to help you achieve that.
How to beat Dodoria as Vegeta
As mentioned above, you will have already beaten Dodoria in battle against Gohan, but Vegeta is ready to crush her. Dodoria isn't much different against Vegeta here, so reading the guide on how to beat him with Gohan first should help here.
Just like with Gohan, you have to watch out for Dodoria's Crushing Fist first and foremost, as it's his most dangerous attack. If you are able to properly dodge the attack, it opens a window like before to attack. With Vegeta in particular, this leaves him wide open to use your Galick Gun attack, which can deal major damage. Otherwise, it may be difficult to connect with Galick Gun, so this is a good opportunity to use it.
In some ways, this fight will be easier because Vegeta is stronger and higher level. However, you also don't have a support character to help you out. Krillin's Sun Flare was particularly useful in the first fight, so you'll just have to go without it. As long as you keep dodging his major attacks and attacking with your own, Dodoria shouldn't pose too much of a threat to you.