Mystina is one of two einherjar Lenneth is unable to send to Valhalla to fight for the Aesir. From the developers' perspective, it's simply because she's required for the A Ending, but there's more to it if you don't look at it so logically. There are a few possible reasons for this.
Mystina's given character traits don't exactly lend themselves to heroism. After all, she's selfish, narcissistic, and prideful, among other things. Hardly traits what one expect in a warrior for the gods! And no matter how much you raise her hero value and improve these traits, if you will, she cannot be sent to Valhalla.
And yet, that doesn't really add up. There are far worse characters that can be sent to Valhalla. Take Badrach for instance — despite being a liar, thief, and murderer, and Lenneth initially planning to send him to Nifleheim, you can send him to Valhalla. Same with Gandar, who's even a boss at the end of a dungeon. So while it could be due to Mystina's personality, it doesn't make that much sense. (The same goes for Arngrim — though he's no model hero, he's not the worst around, either.)
There's actually some Word of God on this that explains absolutely nothing.
Why was Mystina chosen as an einherjar when she seems not to be a very good person?
There are a lot of malcontents among the einherjar, now that you mention it (laugh). The "Heroic value" required for sending a human to Valhalla is nothing more than a human's suitability from the perspective of the gods. Humans with a low heroic value are difficult to control - they don't listen to you from the start.
- from the Valkyrie Profile Material Collection
Right. That tells me nothing about Mystina and only justifies what I said above about much worse characters than Mystina among the einherjar. Thanks a lot, tri-Ace!
Mystina: I'd like to stand atop the summit of Yggdrasil, where it is said that Odin hung as he receives his wisdom...
- from Valkyrie Profile: Lenneth
Mystina's greatest desire is essentially to have all the knowledge in all the realms. The gods, however, might not be tolerant of such a goal. To stand atop the World Tree is a feat far beyond a normal human's abilities, so it's clear she aspires to be more than human. (Perhaps she and Lezard aren't so different after all?)
The knowledge Lezard gave her could also make the gods see her as dangerous. Lezard explained to her the secret of Odin's powers, as well as how one could become a god — not very fitting for a mere einherjar to know. Even Lezard considered Mystina's existence a threat; it's why he killed her.
When Lenneth goes back in time to the Lost City of Dipan, she sees her own former incarnation, Hrist, as well as Hrist's einherjar. Two of these bear a striking resemblance to Arngrim and Mystina — the two einherjar who can't be sent to Valhalla. Could that be why?
As I wrote about in the role section, I can't figure out why Mystina appears in Dipan. If it really was an earlier version of her, though, it might make sense for her to not have to go to Valhalla. She would have already served the gods once before. But then again, a warrior who resembles Llewelyn (if memory serves) also appears, and he can be sent to Valhalla. I must conclude, then, that she only appears there to utterly baffle fans.
Ultimately, Mystina is simply deemed unworthy of Valhalla. Whether it's her ambition, her potential involvement with Hrist, or her personality, she remains with Lenneth in Midgard. And it's thanks to that Lenneth survives Hrist's early awakening, so no matter the reason, it served a great deal of good in allowing Lenneth to be saved.