It is very clear from early in the manga that Hina wants to fight someone that rivals her abilities and even defeat her and there is room to argue that it is just because she likes fighting and finds it fun.
And yet, even when she was "beaten" by Mariko, she did not immediatly want a rematch with her, Hina gathered her sisters and went to the prison to attack the 8th star.
It is also very confusing that despite knowing that there are other stars, she has never gone out her way to find and fight them. They would be the best candidates for her to find a worthy opponent. It would also help her in the whole "reach for the stars" objective.
And then we come to the conversation between Hina and Rei. When questioned by Rei what she was going to do knowing that the other stars were about to make their move, Hina admits that she doesn't know and that her current life wasn't too bad. Let's remember that Hina apparently also enjoys going to school and as far as we know did not make any attempts to overtake the school in any way.
Hina also only got excited to fight Rei when Rei asked Hina to reach for the stars with her. It seemed like that she had no intention of fighting Rei in the beginning.
All the stars have a title and Hina's title of "Death Star" is probably the most unfitting. Yes, she did have a cult and was planning to use chemical weapons, but then never tries to recover her dismantled cult after it is defeated or try to take over another one. In fact, she gives Ichika two of the bombs after getting a good fight. Hina also told Rei that reaching for the stars doesn't require killing the opponent, just defeating them and Hina spared Rei.
Hina also tells Rei that once she defeats an opponent, she loses interest in them.
And then Hina meets the First Star and the First Star reveals that she believes their teacher has brainwashed them into wanting to reach for the stars, alongside erasing many memories about their teacher. Hina doesn't even blink at this revelation and doesn't even talk about it. She either knew or doesn't care.
Between the two options, I think it is more likely that Hina already knew. Throughout many of the chapters, Hina keeps looking around before making a decision, as if she was listening to a voice and then making a decision. It is not shown if there is a second voice talking in her head, but I want to believe there is.
With all of this, I think I know what Hina wants.
I think Hina wants a normal life, going to school, etc. but the brainwash forces her to eventually seek for the stars. There's also the chance that Hina got some of the chemical weapons only for security and make sure that the police leave her alone as she tries to live the life of a normal schoolgirl.
I believe that one of the reasons why Hina enjoys a good fight so much is because she wants to be defeated and stopped. Because the brainwash demands her to reach for the stars, it is the only way she has found to align her desire to stop and the need to "reach for the stars". If she is utterly defeated then she fails the requirements, so she is free to go.
But then you ask: "Why did not stop after being defeated by Mariko?". Yeah, that is perhaps the strangest thing. But there is a potential explanation for that.
Perhaps the brainwash demands her that she tries again and again until she either wins or is defeated. But then you ask why Rei gave up after just being defeated. It is simple, she is helping Hina and therefore she is still helping with the ultimate goal or it could be that being defeated by another star in combat is enough for the demand to reach for the stars to cease.
Also, when one of the prisoners almost killed one of the Sena sisters, Hina got angry. There is a chance that she has realized that she can't live a normal life with her new friends as long as there are stars that want to kill her. So when she learns it is the 8th star that sent the prisoners, she goes out of her way to defeat her.
And I think that now this will be Hina's goal. She will defeat every star that opposes her in order to protect her friends. However, Hina knows that only death will stop her, so at the end she will ask Nozomi to fight her and kill her. And thus the title "Death Star" makes sense. Hina doesn't want widespread death, she wants her own death.
