Very nice.
About time someone went and did this. I have to give you kudos on this one, it certainly looks like you put a lot of work into the art/animation. Anyone can make sprite cartoons, not everyone can do this.
My only beef with this (and what subsequently kept this from a perfect score) was during the fight scene. At several points, there was just too much going on with too many view shifts. While the controlled chaos is a fantastic effect that emphasizes intensity, I think it was just a bit too much here and there. Various parts I had trouble deciphering just what was going on.
The audio goes without saying, a bit of volume control on the explosion noises would curb a lot of comlpaints, but you already are aware of this.
As far as the plot idea - Chrono Trigger's been around so long and had so many fanfic type plots that criticizing (Constructive or not) it after such a comparatively small amount of exposure would be counter-productive.
Anyways, that's all I got for you. Grats on the finished product, and I look forward to more of these. :>