Here is a list, which I will edit periodically, of all playable monsters that I have seen or shrined so far.

Antlan/Antlan
Antlan/Psiroller
Antlan/Suezo
Antlan/Raiden
Baku/Baku
Baku/Garu
Baku/Lesione
Beaclon/Beaclon
Beaclon/Ducken
Beaclon/Zuum
CP/CP
CP/Antlan
CP/Baku
CP/Madillo
Ducken/Ducken
Ducken/Henger
Ducken/Naga
Durahan/PsiRoller
Garu/Garu
Garu/Hare
Garu/Naga
Garu/Ripper
Garu/Suezo
Garu/Tiger
Gitan/Gitan
Gitan/CP
Gitan/Suezo
Golem/Golem
Golem/CP
Golem/Gitan
Golem/Henger
Golem/Jell
Golem/Raiden
Golem/Suezo
Golem/Zuum
Hare/Hare
Hare/CP
Hare/Durahan
Hare/Madillo
Hare/Raiden
Hare/Tiger
Henger/Henger
Jell/Jell
Jell/Joker
Joker/Joker
Lesione/Lesione
Lesione/Beaclon
Lesione/Dragon
Lesione/Mocchi
Lesione/Naga
Madillo/Madillo
Madillo/Beaclon
Madillo/Mocchi
Mew/Mew*
Mew/Baku
Mew/Hare
Mew/Tiger
Mogi/Mogi
Mogi/Garu
Mogi/Mocchi
Mogi/Suzurin
Naga/Naga
Naga/Henger
Naga/Plant
Naga/Suezo
Naga/Zuum
Ogyo/Madillo
Ogyo/Zan
Pancho/Pancho
Pixie/Lesione
Pixie/Suezo
Pixie/Tiger
Plant/CP
Plant/Pixie
Psiroller/Psiroller
Psiroller/Baku
Psiroller/Dragon
Ripper/Ripper
Ripper/Durahan
Ripper/Tiger
Ripper/? (Nightseeker)
Suezo/Suezo
Suezo/Hare
Suezo/Jell
Suezo/Lesione
Suezo/Pixie
Suezo/Tiger
Suezo/Zan
Suzurin/Suzurin
Suzurin/Ducken
Suzurin/Mocchi
Tiger/Tiger
Tiger/Henger
Tiger/Madillo
Tiger/Zuum
Zan/Zan
Zan/Madillo
Zuum/Zuum
Zuum/Baku
Zuum/Plant
Zuum/Psiroller
Zuum/? (Dino)

* Nya/Nya for purists....