This is already pretty good.
There's a lot to learn so the very start is pretty overwhelming. Having the levels gradually add animals could help, even if you split it out into a mode besides the true challenge-run.
The other thing is that the fights are a little hard to follow. I think snappier movement but then slightly longer delays would feel better, and maybe displaying moves one at a time but still simulating them the same, if that's possible. Little blip sound effects would make it feel better too.
It would maybe be fine to show stats without mouseover all the time, or at least have an option for it.
But yeah I really like it. I'm gonna play some more and keep an eye out for updates.