I think a lot of us - myself definitely included - get confused sometimes, about what the point of all this is. Why we do this "PPC" thing, these missions. The mocking, the snarking, the jokes, they're all to make ourselves laugh at something that would otherwise be annoying or angering.

The point of concrit is to help the author improve. Nobody spends hours writing a story if they don't want it to be read, enjoyed. Some authors can take criticism well, some cannot; some are good writers, some or not. But the thing is, if an author cares about their story, and is willing to take criticism, just make it very clear what your intentions are. You don't want to tear her down, you're not making fun of her, you want to help her make her story better.

Intent is not magic, of course. But if you make it clear, it does count for a whole lot with most people.

If she's willing to learn and improve, I'd start by making a list of the most egregious canon errors to discuss, especially things that can be altered fairly easily (eg if moving the fic to Mirkwood from Fangorn won't need any more changes than the name).
If she's not willing to learn and improve, give it up for a lost cause before you get too invested in her.

I had a problem similar to this on DeviantArt. She hasn't actually written anything, but she's drawn the characters and they are very Sue-y. I found out about them through this journal entry of hers. It gives a pretty good description of why the characters are Sue-y. Then, she posted pictures of her characters and asked for critique, which I gave. Since I don't think I offended her, here are the conversations I've had. Hope they help you have a civil conversation with "ShadowfaxRunner".
The first conversation, on the picture of the primary Sue's sister : http://ladydata.deviantart.com/gallery/#/d5qzbke
The second conversation, on the picture of the Sue's mother (if this was a fanfic she'd probably be recruitable) : http://ladydata.deviantart.com/gallery/#/d5qz9u8
And the last conversation, on her forum topic "What is your opinion about OCXCanon fan pairings?" : http://forum.deviantart.com/art/literature/1824241/

My sympathies. As I have found, communicating with Suethors (or possible Suethors) can be difficult.

Maybe you could ask if she's open to concrit, and make sure she's aware that's going to mean pointing out errors along with ways to fix them? Then maybe start with a general thing (e.g. "you've got some canon details mixed up") and see what the reaction is. If she goes "oh, I know, but it's my story and I can change things if I wanna," or otherwise doesn't care, then you're probably not going to get anywhere. If she's really interested in fixing things, though, then you can proceed to specific problems.

That's just my two cents, though; others might have other ideas.

~Neshomeh

Cut down the snark and explain what's wrong with the things you found. I know it's going to be quite a list, but if there's many things wrong with it, so be it.