Each character has two parts. The first is an outline, probably used for intro and/or battle text.
The second is the actual character.
There might be a couple blocks I haven't properly decoded (I know one of the blocks that didn't dump correctly was the kana, but I can identify those.

Thanks for any help.
Thanks BRP for the first 256.

I've used radical lookup and Global IME to fill in most of the remainder of the table.
Could use some help with the last ones.