Well...? I'm waiting for the full thing!
Before I go into review details, I first want to say that Elfen Lied was one of the best manga I've ever read. The concept of the vector arms was original and most of the characters were great to have in the series.
The flashback part was well put in the middle of the story and I must say, you've animated that quite impressive:
Art/Animation: 8/10
No bullshit, you just animated the (emotionally) most brutal part and did a fine job at that. I disagree that it looks old, this looks just fine. The colors 'made sense' and the emotions were (fairly) well drawn. I'd like to mention, however that the movement of the... loose bodyparts and the blood were done a little unnatural. I'm not sure how hard it is to make that more realistic, but that's a slight reminder from me.
Music/Adio: 9/10
Not THAT bad quality and it fitted well. I would have liked some more music (at the silent parts, apart from the bloodshed you can make the music softer).
I'm not gonna review concept, since this is from another story and it's a teaser, so here's the total score:
Overall that makes an 8,5/10 rounded up to a 9/10 and a 4/5. Keep it up and please send me a PM with the link to the full version, because I'll definately forget to check... Sorry :P