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When Captain Marvel has acquired her full powers, we see her able to do many things. Fly, shoot energy out of her wrists and more. She even flies into outer space... but doesn't she need to breathe?
There's no visible helmet on Captain Marvel when she's looking at the ship in space and when she flies out of the Solar System.
She's still human and therefore, still needs oxygen. But she's clearly out of Earth's orbit and atmosphere.
The short answer here is because Carol Danvers, as Captain Marvel, has the ability to fly and breathe in space. This first came about in Uncanny X-Men Vol. 1 Issue 164 when she transforms into Binary and we see her blast out of a space ship into outer space without anything protecting her face.
Click image to enlarge.
She then mostly keeps that power, we see it in the more up to date comic issue of Captain Marvel Vol. 8 Issue 6 when she's flying in space.
Click image to enlarge.
And just to be extra clear here Marvel.com even states she has the power to fly, breathe and survive in space.
Flight in Space
Captain Marvel has the power of flight, which she uses in tandem with her ability to breathe in the vacuum of space to journey at super speed throughout the cosmos.
The fact is that in the films we see Carol in she can breathe and fly in space, true to her comic origins, so lacking any contradictory evidence we have to assume it is one of her powers like in the comics. It too would have been given to her by the Space Stone/Tesseract/light speed engine during the explosion.
Carol also has her binary powers in the films so again with it staying true to the comics it makes no sense for her not to be able to breathe in space and would only complicate matters for production with her needing a helmet on at certain times and not others.
In The Road to Marvel's Avengers: Endgame - The Art of the Marvel Cinematic Universe we get a brief section on Carol and as part of it we get the following excerpt. Whilst Andy Park doesn't out rightly say she can breathe in space, he does say she is "invulnerable".
Captain Marvel - A.K.A. Carol Danvers - is one of the strongest characters in the MCU. "Captain Marvel's whole power set is very unique," Directory of Visual Development Any Park says. "We've established so many characters up to this point after ten years of the Marvel Cinematic Universe, but we never had a character like Captain Marvel. She's touted to be one of the most powerful Super Heroes - and in a lot of ways, the most classic, comic-book-y kind of character. She can fly. She's invulnerable. She can shoot photon blasts out of her hands. And it's not because of some technology or because she's wearing armor."
Perhaps I'm being a bit technical, but I don't believe Carol, or other space-fairing, non terrestrial beings like the Silver Surfer, Nova, Thanos, and even DC heroes like Superman actually "breathe" in space, per se; they function in space and their muscles may actively pull in and out... but with no known atmosphere, they aren't technically "breathing." As to how they can maintain that kind of functionality... I do have a theory.
First we need to understand why humans breath in the first place, how it effects the body, and why it is necessary.
Without going too in-depth, the process of respiration, essentially, is needed to create energy (or more accurately, "release" energy) within human cells. Our bodies adapted to do this by taking in oxygen in the atmosphere, drawing it into the lungs, where it is diffused into the blood stream and sent to all the cells in throughout. Basically, it's one big, continuous chemical reaction which evolved to facilitate cellular survival. A simplified diagram of it can be seen here....
Now given the intricate nature of this chemical reaction, I'm bypassing a lot of information here, from the release of ATP to functionality of mitochondria within the cells to generate energy via a reaction with oxygen and sugar....
Main Point to Remember: Breathing, aka, the act of respiration, allows our human bodies to produce and release energy.
This is where the differences come in super heroes; their bodies may be humanoid and even genetically mostly human... but due to their super normal abilities, many can bypass the "need" to respire in order to create this energy. Carol is up there in this class of hero; her physical structure doesn't "require" oxygen to facilitate its other energetic functions.
This would seem to be backed not only by Carol's ability to sustain herself, unaided, in the temperature extremes of space, but to "feed" of other energy sources, "go Binary" and increase her powers. Essentially, her body is "generating" or absorbing the energy directly, and thus feeding her cells without the oxygen as a catalyst for the release process. The fact that other beings with enhanced durability or energy projection processes can do this too supports this claim. Thanos doesn't need to "breathe" to survive; Silver Surfer's molecular structure was altered and augmented by Galactus's "Power Cosmique" to be changed on a fundamental level, requiring no food, water, or sleep...he can just feed of the latent energy of stars.
The case of Superman is especially interesting, in that apparently he could always exist in space without air... he just had to "learn" to trust his body to do so. His Kryptonian physiology is capable of sustaining itself in perpetuum once any level of sunlight orange and above is available to him. Still considering himself a "man of earth", however, Clark unconsciously limited himself by thinking he "needed oxygen" to survive in space. A little training from Mongol II laid that fallacy to rest...
Whether Clark was actually breathing within the vacuum is unclear, but what's made apparent is that due to his body's ability to sustain itself, actually oxygen intake was unnecessary. However, these are all comic book based examples.
Bringing this back to Captain Marvel (and I'm presuming you mean the film version here) the reasoning is still basically the same; Carol's body is producing its own energy, or at least sustaining itself in some way due to the energy her body can generate, or repeatedly absorb. We've seen her use or "give off" this energy as it surrounds her body, burning or creating an observable glow in space sans any form of oxygen...
And considering that this version of Captain Marvel was empowered by an Infinite Stone... a powerful object which has been shown in-story capable of altering living beings on molecular levels, as well as warp everything from Space and Time to Energy and Reality... it's not surprising that Carol's tissues and nervous system may have been changed to the point where the need for oxygen is now superfluous. The stone in question was the Space Stone, however, so I'm a bit unsure how that could account for her ability to breath in space exactly, but the stones have been shown to have multiple other affects.
I have two theories.
I don't remember which movie it was in, but at some point they talk about the Tesseract being a source of unlimited, clean, and sustainable energy. Since it was the Tesseract Carol got her powers from, she has that same ability. She didn't absorb all of the energy from the Tesseract, but even 0.001% of infinity is still infinity. The power she got from the Tesseract goes directly into her cells. She can breathe if she wants, as we see her do any time she's on Earth, but she doesn't need to.
Since the Tesseract is jut the Space Stone covered in a fancy glass cube and she absorbed some of the power from it, it may be that her powers are protecting her by teleporting oxygen into her lungs when she's in space. That doesn't mean that she has the power of teleportation because she can't control that. It just happens on its own.
the answer regarding the need to breathe is above its basically not even to produce energy in the form of ATP (the energy comes from he binding and breaking of the 3rd phosphate group i.e. ADP, adenine di-phosphate to ATP adenine tri-phosphate) the reason we need oxygen is due to the by product of the main production of energy this is hydrogen! so during the main part within the mitochondria we are left with H+ atoms so we need these to be "mopped up" O2 is used it binds and produces h2O or water. this is the only reason we actually need oxygen and it is to produce energy. so if you can produce energy another way than through the process of respiration then you do not need to breathe! and that is basic science fact! so funnily enough the question of breathing in space is a super power that can easily be explained and techincally could be done (with advancements in science!)
