Namely, her annoyingly tragic "the last survivor of my people" cliche, the fact that she is a crossbreed between two species that have never been even implied to be interfertile, the aforementioned invisible tattoos, or the fact that she is changed into a shadow beast but keeps an intact mind due to her "mixed blood".
In fact, the very possibility of a Twili and a Hylian(I can't find anything saying what her other half is, only that it was a female native of the world of light, but I'm going to assume it's Hylian because being part surface human isn't speshul enough and none of the other races more than faintly resemble Link. I guess she could be part Gerudo, but she'd probably have angsted about that because Ganondorf is a Gerudo and Sues tend to believe that morality is bloodborne) meeting for long enough to bear a child is preposterous enough, from a canonical standpoint. The Twilight Realm was intended as a prison plane from which no one would be able to escape without being released from the outside, ipso facto, no random Twili would be able to just wander into a Hylian village and mate with people. Zant was only able to get out by using a mix of Twilight Realm magic and the Triforce of Power energies that Ganondorf gave him, which was a combination that the Light Spirits who imprisoned the Twili most likely wouldn't have anticipated. Nyx's briefly touched-upon backstory implies that her father just left somehow, sired her, went into exile on Snowpeak, and was killed by the barbarians that later raise his daughter because he "didn't belong here". That raises so many questions, not only on the hows and whys of the escape, but why the barbarians didn't kill Nyx as an abomination, or why she doesn't feel anything about the fact that her biological father was killed by her surrogate family for being a foreigner.

That's a very implausible backstory, to sum up, and I made my judgement too quickly because I didn't know about it. If it were me, I'd say that she seems to have done too much damage to canon to be recruited, in combination of the little distortions and the larger matter of the way she arranged the circumstances of her history.
Since it's not me, I would recommend two things: one, play Twilight Princess all the way through before sporking this, or at least the rest of the way through from where you left off. It's not good to go into a mission for the Protectors of the Plot Continuum with only partial knowledge of the plot that's being protected. Two: if you do decide to recruit her despite everything, the Flowers are going to be very angry with you. Recruiting the central Sue of a mission has only happened twice, as far as I know(a few Agents were recruited as Sues offscreen, but even then it only raises the number to about six or so), and both times the Sue wasn't nearly as bad as the story around her. In this case, the Sue is everything bad about the story, since without her, it would just be a fanfic that stays near canon in just about every fashion, with the only significant deviation being that Link can talk. You will need to address this. On the plus side, this means that her planned eventual assignment to your RC could be the Flowers deciding that even though she went through Agent training without maiming or Sueifying anyone, she still needed to be supervised, and the best people to do so were those who thought recruiting her would be a good idea. On the minus side, your Agents are going to be getting horrible, horrible missions into perpetuity as punishment for their transgressions(probably out of the Circle), not to mention that they would never be in what passes for the Flowers' good graces again if they recruit that level of Sue on their first mission together before proving that they know what they're doing. At the very least, it would take a while and they'd need to prove themselves competent to their superiors.
She might also need to settle into one of her two ancestral species, both as a way of rejecting her Suvian heritage and because, again, those species were never meant to mix, but I'm not sure how you'd go about accomplishing that.

By the way, if it says that she's a "shadow beast" in-story, she's going to look like a shadow beast, especially since she doesn't seem to have full description of herself in beast mode, just that the form's furry and about the size of Wolf Link. That's the way the Word World works. It takes the Words that comprise it very literally.