I don't feel like people have a nuanced enough view of Kory what she thinks about killing. She's not blindly wanting to murder criminals, nor is she delighted by the actions of murder. She sees murder as a necessity because of her upbringing in the middle of an existential war, and also as a way to regain autonomy on her life. Autonomy is a key theme in many of the people Kory chooses to kill.
The idea of autonomy over the body and her life is extremely important to Kory. This makes sense, Kory spends six years in slavery, her life not her own, and grew up knowing her planet could lose its own autonomy and freedom at any time.
When she was a slave, the few times that she was able to control her life in those times. Her first kill was her kill of what would become her last master, starting the chain of domino that would result in her freedom.
Note her words: "His very touch sickened me". It wasn't just about her imprisonment or her anger, but about her body, her autonomy. She couldn't handle being touched like that anymore, and killed knowing that it would solve nothing, knowing that it would lead to more punishment for her later down the line.
Her next kill allowed her to escape, securing her freedom and her own autonomy.
To escape she must pretend Kory has completely given in to her captors. That she is fine, even happy with the Gordonian touching her. But by doing this she is bringing him close, giving him the illusion of control over herself to secure her own freedom.
She is pretending to be a slave, while affirming to herself that she is still a soldier.
In this way we can see a dichotomy that has ruled Kory's life until now. On one side, you have succumbing to subjugation, which involved a loss of bodily autonomy. On the other side you had her claiming her freedom and her autonomy which comes with the need to kill or be destroyed.
In addition to this, you need to think of the context of Kory's upbringing. Of course Kory is used to killing her enemies. She grew up in a climate of fear in which there was a real possibility of total annihilation. Millions of her people died in the war that eventually lead her to being sold as a slave.
She grew up during a society that could have been destroyed in war, where everyday killing was not a questions but an existential threat. Killing and war was literally the only way for her people to conserve their autonomy.
This disconnect between Dick/Donna and Kory is not because Kory is an alien, but because the Titans are living in a world where they are superheroes and Kory is living in a world where she is a solider. Would a Kory that didn't kill even been able to come out alive from war? From her enslavement? To her its about her autonomy and her independence, she doesn't have the luxury of morals, of thought, of choice.
Later we see Kory not change, but shift. She realizes that killing will never be easier for her again.
This makes sense! her interpretation of killing has changed a lot because she's been exposed to a new environment. On earth she is not facing a literal war, she has real power, she has backup, she doesn't have to fight every second for her freedom and autonomy.
I think this is demonstrated in an incredibly narrative compelling way in Titans (1999) when Kory kills to give another character autonomy over her own body; Adaline Kane. Adaline is about to die, but her blood can still be harvested for Vandal Savage's experiments. She begs for death, instead of living that fate.
(much like Slade gave Joey in Titans Hunt but this post only has the space for one parallel right now)
When it comes to protecting the greater good, and especially when it comes to bodily autonomy Kory is not only willing to kill, but sees it as her duty.
She's never stopped being a soldier, she's never stopped being the Tamaranian who was forced to kill and see her people die to preserve her home, but more than that, she never stopped being the little girl for whom killing was her only way of reclaiming her autonomy.
