Good god, I'm long-winded:

Hi there. It looks like you're trying to avoid making Alexandra a Mary Sue, which is great. Since that's the case, I thought I should tell you there are already some pretty common Sue warning signs present. I realize it's only the first chapter, so things may change once the plot gets going, but let me point them out:

First of all, women cannot currently join the Navy SEALs, so the fact that your OC did means one of two things:

1) this story is set in an alternate universe where they can,

or

2) your character somehow got in anyway, making her more special than every other woman on the planet for no explained reason.

I don't think there's much point in starting your story in an alternate version of Earth, since Alexandra is going to end up in Middle-earth soon, so that just leaves the second possibility. Unfortunately, a character who is automatically more special than anyone else just by existing is part of what makes a Mary Sue. If you'd like to make your character more believable, I recommend choosing a branch of the military that actually is open to women at this time. (We can hope the SEALs do admit women in the future, though!)

Second, Alexandra has the looks of a fashion model. I will never say that a woman can't be in the military and pretty-she certainly can-but the requirements of your basic fashion model and a soldier are quite different; the two body types are mutually exclusive. If she really had the soft, slender body of a fashion model, she would never meet the rigorous physical qualifications necessary to join an elite fighting force. Furthermore, all the branches of the military have uniform codes, and curls of hair that could get in her face and distract her in combat are right out in all of them. Right now, with the job she has, her looks are impossible in the real world: another big Mary Sue warning sign when your character is meant to be from Earth.

Third, winning people over by singing is a pretty typical Mary Sue trait. Singing is fine, lots of people sing; however, beware of making other characters instantly like Alexandra just because of her voice. Even nasty people can have beautiful voices.

Now, none of these things by themselves will make your character a Mary Sue, but all of them together are an almost guaranteed recipe for Sueness. The good news is it's easy to fix at this point: just choose a more appropriate branch of the military and some more realistic descriptions, and you're all set. {= )

As you go on, the main thing to be careful of is that you don't give your OC everything too easily. It looks like Legolas is going to be a main character as the story goes on. I don't know what your plot is, but I see Romance up there, and since lots of stories are about girls falling in love with Legolas, let me use that as an example. If Alexandra meets Legolas and he's immediately impressed by her elite skills, good looks, and fantastic singing voice, that's not going to be much of a story, and it won't give your readers any chance to sympathize with her. If she already has every advantage, there's no question about whether she'll get a happy ending. A character has to have some kind of real struggle in order to be sympathetic.

Let me put it this way: is it nicer if Legolas is the kind of guy who falls for the picture-perfect fashion model girl with impossible status, or if he falls for the normal girl who worked really hard to get where she was, and had to fight to earn the respect of the guys in her troop, only to have it all whisked away from her in one horrible twist of fate, landing her in a strange world where she doesn't even speak the same language? (That's right: nobody speaks English in Middle-earth. The ones who don't speak Sindarin or Khuzdul mostly speak Westron.)

I know I'd much rather read about the second girl, myself, and I think Alexandra can be that girl with just a few easy changes. {= )

This review has gone on long enough, but please feel free to get in touch if you'd like to talk more. {= )

~Neshomeh

We'll see how that goes.

Looks like a Sue-wraith instead of an actual Sue, but it's powerful enough to overthrow the Valar. Fic's still in progress, though.

Fly Away
http://www.fanfiction.net/s/5309095/1/Fly_Away
"When the death of his father goes unpunished, Fëanáro overthrows the Valar and establishes his own dynasty. His half-brothers' children, determined to oppose him, are drawn into a dangerous realm of intrigue as they work to bring his rule to an end. AU"

I'll keep my eyes open. After back-to-back Angst!Sues, I've been looking for someone who'll give my agents a fight.