I'm sorry to see that someone has labeled this story as Sue-ish. It's always a blow for an author to see that, and it doesn't actually give any help on how to get better. However, I do have to say that Sabrina has many, many Sue-like qualities. You seem to be ramping up for what could be an interesting story, hopefully one where SN learns to reach out, and have stable emotional relationships.
The problem is going to be that no one will want to read about her attempts to become more "human" because aside from that one glaring personality flaw SN is perfect. The fact that she could beat Ash with one hand tied behind her back is uninteresting. Or, I should say, it isn't enough to hook the reader into caring for this prodigy. Someone who has already achieved what should have been an interesting march on the pokemon universe is someone whose story has come to an end. Also, realistically, we never tackle our problems one at a time, so SN is not going to have studied all she can, then beat the pokemon league, then start dealing with her own emotional problems. They will have been a difficulty for her since she became aware of her father's death, just as the fact that she will -- hopefully -- have not dropped all of her studies when she started journeying.
To get to the individual chapters, I have trouble conceiving SN in chapter one as a great strategist when she uses a ghost type attack against a dark type, and then tries to use slash on a pokemon who is in mid-air. I realize that her unnamed absol is powerful, but of the volley of attacks that are available to an absol why not use the neutrally matched "Razor Wind" to knock the murkrow around, and confuse it, rather than try a direct physical attack? It seems as though her real strategy is to power her way through her opponents, which is not realistic to what you build her up as in the second chapter.
Speaking of which, the back story on your prodigy could be toned down a little bit. Is it really that impressive that she has memorized all 493 pokemon? Most people who play the games have done the same thing, and in less time than you imply it took her. I feel that it would be a lot more impressive if she had only one or two astounding achievements to her name, and was working toward others: For example, capturing heatran, or something. One of SNs weaknesses is that she has no more goals to strive for in her life. It is pretty dismal to say that you've accomplished the best/most difficult bits of your life by the time you are 13. There does not seem to be any room left for growth in her chosen field.
One question: why did you switch from past tense to present between chapter one and two? It seems oddly inconsistent.
Finally, there is a problem of saying, not showing. SN, and the narrator both say that she could wipe the floor with Ash, but since when has that been a feat, and how do we actually know that she can do it? I could say I was Prince Lucian of the Moonlight Knights of the Cross, but that does not actually make me PLotMKotC. It would help if we knew that she had encountered Ash at some point, and wiped the floor with him. And instead of saying just that, it maight be nice to see it happen in flash back form. In fact, most of chapter two could be convincingly re-written in a series of vignettes to convey how smart, well studied, tragic, powerful, companssionate, lonely, and isolated SN is.
To wrap up, this story is good. It has the beginnings of something that could actually go somewhere. On the other hand, it needs some clean-up/de-sue-ifying. If you want some more hints on what not to do, look at this litmus test for fanfic characters:
A lot of the questions are leading as to ideas that show when you might be going just a little too over the edge, and their de-sueifying suggestions are good.
There is also some good advice to be had on this forum, although the solution provided is a little harsh, in my opinion: http://banette.proboards51.com/index.cgi?board=general&action=display&thread=1&page=4#61
Anyway, I hope to see more of this fic, and want you to keep on writing.