Your sample dialogue sounds unnatural because it's on the nose. If you're not familiar with that term, it means, essentially, that there is no subtext. The characters say exactly what they think, feel, and mean; and they do it in a perfectly articulate manner. The reason on-the-nose dialogue is bad is because humans generally aren't articulate.
Sure, someone who is naturally charismatic or a highly practiced public speaker is capable of being articulate in this manner - but even then, they do much better when prepared than in the heat of the moment. Most people, who are neither trained speakers nor gifted with exceptional charisma, are going to have an even harder time expressing themselves clearly. Especially in a tense, emotionally-charged scene, people aren't taking the time to think about what they're saying or how best to clearly express it. In real life, people stutter, hesitate, cut themselves or each other off, talk around sensitive subjects, or refuse to talk altogether.
To assess whether dialogue sounds unnatural or cringy, examine how easily your characters are conveying their main points. If they're speaking with perfect clarity about exactly what they think or feel, your dialogue is most likely unnatural.
To apply this to your sample dialogue:
Natalia: You turned me into a monster, how could you do that to me?
She's addressing her concern exactly: that she's been turned into a monster. Instead, have her dance around it - talk about how she can't go out in public anymore, or even just have her be non-specifically horrified.
Robert: It was the only choice! You think we could have survived
otherwise? I made the call, because of that we're both alive. How
can't you see this!?
He immediately understands her concern, articulates his reasoning perfectly, and makes an immediate counter-argument. But if she's already hedging around the subject, he'll have to work harder to understand why she's upset - maybe even get it wrong at first.
Natalia: You made the choice without letting me decide my own fate. I
cannot ever forgive you for this!
Again, she's clearly explaining why she's upset about this. If this is a new situation, she may not even have figured out yet that the lack of choice is what's most upsetting about this. You could have them argue back and forth for a while longer while she slowly realizes that this is the crux of the issue.
Robert: I don't care! Do as you want. If you want to die, go ahead,
kill yourself. It's as simple as it gets. No matter what you tell me,
it's not going to do any good. What's done is done!
He's getting to say too much. If Natalia is truly as upset as she sounds, she'd have interrupted him by now.
Natalia: You pig!
Aside from the fact that this retort doesn't make much sense in context (usually calling someone a pig means they've been crudely sexist or otherwise gross, as opposed to morally or ethically faulty), it's too mild for the argument up til now. If she's really so mad about what he's done, she'd have some stronger words for him - or she'd nope right out of the conversation in fury.
Natalia: What have you-- Oh my God. I'm--I'm-- What am I? What have
Robert: Hey, wait, you're mad at me? What for? I made you stronger!
You're powerful now! You can save us!
Natalia: But I'm... I'm... This isn't right. I didn't want this. Why
did you do this to me?!
Robert: I wanted to survive! I wanted both of us to survive!
Natalia: I don't want to survive like this! If I had known surviving
meant becoming a monster, I never would've agreed!
Robert: I was trying to help! Do you want to die?
Natalia: I wanted the choice!
Obviously not perfect as I don't know the details behind the situation and am writing this off the cuff, but the point here is to add layers of subtext, confusion, and implication so that the conversation builds up to a climax as both characters slowly realize what the true issue is.
The key is to remember that humans almost never express themselves clearly and perfectly on the first try. If your characters are speaking articulately about the exact issue(s) at hand (even if they're being emotionally heated about it), your dialogue is likely on the nose. Add subtext, inferences, implications, misunderstandings, and other layers to give your dialogue the depth of real human speech.