I take issue with your implication that participating in battle requires so much more mental strength and courage than anything else, including being a woman in the Middle Ages.
And yes, this is completely relevant: you asked about Joan of Arc, a teenage girl who convinced a king to let her lead an army, instead of all the men who were conscripted into armies against their will.
One of our most popular questions on AskHistorians is, "Did/how did medieval soldiers deal with PTSD?" The question we have never gotten is: did rape survivors in the Middle Ages deal with PTSD.
That is not to say that 100% of women in the Middle Ages survived rape or attempted rape. It is to say that women like 15th century brewster, intrepid traveler, wannabe saint, and first autobiographer Margery Kempe--who, if we believe her account, stood trial for heresy and won--insisted that another woman spend the nights with her even with the window locked. It is to say that thirteenth-century (actual, not wannabe) holy woman Lutgard of Aywieres faced immense social scorn because of a rumor that she had been raped, and hid inside her father's house. It is to say that every woman in medieval Europe dealt with pre and non trauma of being violently sexually exploited even without picking up a sword.
And then there's Joan herself. Joan before and after she was a warrior-prophet does not get nearly enough credit today.
Although there's a bit of myth packed around this, Joan was in all likelihood a middle/upper-ish peasant whose father was quite well connected in local politics. She probably learned to read, at least in French, despite single-digit literacy rates among peasants (Some people have tried to deny this, despite the fact that she passes the exact retrospective literacy test scholars generally consider too strict.) She was apparently also quite adept at riding horses.
Joan was no isolated country kid. Her trial testimony (we'll get to that part) shows her to be right in line with the international religious trends of the time; even at the forefront of some of them. The saints whose voices she declares she hears are St. Katherine and St. Margaret, basically the two most popular women saints (besides Mary) in the late Middle Ages.
She also mentions visits and guidance from the Archangel Michael--a somewhat common presence in medieval Christianity, but the fifteenth century was really the age of angels. (The concept of a "guardian angel" is developed in the writings of wildly influential theologian Jean Gerson, an exact contemporary of Joan who defended her.)
You can pick out of her words a devotion to the IHS as a symbol, the name of Christ (Ihesus in Latin)--another mid-late 15th century development.
Now let's look at how Jeanne got from Domremy to the battlefields.
Her authority and access (things granted by other people) were built on two things: her charisma and her prophecies that God would guide France to victory so long as the king didn't give up. Joan had to deal with a progressively more powerful series of nobles who, essentially, gave her permission to reach the next as well as physical aid (like, you know, a sword) to do so. This chain included nobles who didn't believe that a teenage girl could/should advise a king on military affairs, and so she had to persuade others to get them to help her.
Then she had to convince the actual king of actual France to let her lead or help lead an actual army in actual battle, nbd.
Joan stood on solid precedent of having people listen to women who asserted the divine source of their messages, although those messages tended to be, "The end of the world is coming unless you repent" or "look how holy I am." But there's a wrinkle. By the 1420s, there was also serious opposition to holy women in most of Europe, especially as public figures. In fact, Gerson's defense of Joan has a lot to do with--essentially--him defending her from his earlier attacks on women visionaries and prophets. That's on top of France being one of the less-welcoming countries to holy women in the first place.
Now let's move on to her time with the army even before battle. Remember what I said about rape?
Joan is pretty explicit in her trial that her famous donning of men's clothing has a lot to do with protecting herself from sexual assault. Her virginity--which means, her not being raped--was so important in people's eyes that they assigned her the nickname of "the Maid."
It was so important in people's eyes that at her rehabilitation trial (after her death), one of her male supporters testified that he had spent the nights next to her in camp...and God's protection of her virginity was so strong, he hadn't felt any sexual attraction towards her. But every moment, Joan had to deal with the fact that for medieval soldiers, raping women was basically a right, was part of their salary (#NotAllSoldiers, of course). She had to withstand the fear of everything crashing down because of an omnipresent thread over which she had absolutely zero control.
Fast forward to her (actual) trial. She was a nineteen-year-old girl on trial for life and almost certainly knowing she was going to lose, facing a large panel of hostile judges.
Our best source for Joan's life is, in fact, her testimony at her trial/interrogations. Despite the nature of the source as recorded by someone else, medievalists consider it a fairly accurate representation of the questions and answers. And Jeanne...snarks the living daylights out of it.
She'll go down the path of her interrogators' questions just enough to tantalize them, and then suddenly say, "I'm not going to say anything further." She would say, "I can't talk about this now." The so-called French minute, the trial record, would be a great read if it wasn't so tragic.
Also, when Joan was captured, she was carrying a sword that had formerly belonged to a Burgundian soldier. In other words, there's a good chance her sword had been taken from the dead body of an enemy soldier.
All of that evidence of Joan's mental, emotional, and spiritual fortitude stands separate from her belief that God was driving her to do all this, that God was requiring her to do all this.
As to your second question: The biggest historiographical truth or misconception about Joan has nothing to do with whether or not she fought in battle, or whether or not she had military training. It's the misconception that she was nothing else except her ability to fight or not. Jeanne d'Arc of Domremy was so much more. So the real question isn't how could she withstand the horrors of the medieval battlefield. It's how could all the men around her.