I don't hear a *recording* problem. It might not be the best mic for her. There's a bit of a high mid boost that she doesn't need. If you try to EQ it out, you lose the high overtones on the earlier passages. I'd put an Oktava MK319 or an AKG Solid Tube in front of her, and avoid almost any Chinese miic. It's also somewhat annoying when she sings to *the camera*. That's lovely for the video, but is not so good for the recording, as she moves on and off of axis. She needs to understand that her "audience" is a 1" piece of gold-spluttered mylar, and simply *stand still* and *sing to the mic*. Learning to do that is one of the hardest things about making the transition from a performing vocalist to a recording artist. In the beginning, there's a tendency to lose the emotion if you can't move, but you get over it. The *mic* doesn't care about how cool her swaying, hand gestures, and touching her hair are. It only cares about where her mouth is and where it's pointed. I also agree with those about how much more powerful her voice would be if she got it out of her throat and sang from her diaphragm. Lastly, her diction is sloppy, and she can hardly be blamed for that, as the majority of current pop superstars have the same problem. It's worth comparing the diction of Mariah Carey or Beyonce (sloppy diction) to Michael Jackson or Madonna (not sloppy).
So- my advice to her- stop moving, sing from your gut, pronounce the words as if they meant something, and *then* learn to do all of that without losing the feeling. The mic *listens* to you, it doesn't *look* at you. My advice to the OP- The sound you hear is coming from *her*, and the mic brings out parts of it that you don't care for. Either change the mic, or learn to like it. Whether she's doing it on purpose or not, she's doing it. And just so I'm not misunderstood, I think her voice is lovely, and for her age, she's very good. She just needs to learn that the skill sets of a performer and a recording artist are different. That's one reason why so many videos are lip synched, so the artist can move, gesture, dance, and look pretty, without screwing up the recording. In the studio, it's all about the mic.-Richie