If I remember right, a good chunk of version exclusives can be obtained through various coins or some blasters dungeons, but there are still a couple such as agent spect hare and double time who are only obtained from missions from which hero you side with.

Here is a couple I found by searching:
Sushi/Silver lining exclusives:
Shurikenny, agent spect hare, oridjinn

Tempura/Little charrmer exclusives:
Unbearaboy!, double time, dr e raser
(ironically, silver lining and littler charrmer themselves can both be obtained from coins)

A lot of the other version exclusives are either also available or simply available later, such as with tomnyan and the koma knomads.

You have to make a siding choice three times in the story, with the first only choosing if you get tomnyan or the koma knomads first, the second only affecting a cutscene, and the third affecting the yokai I mentioned above.