Monster Farm: Enbanseki no Himitsu (1999)

Genki is a boy who loves playing video games. One day he's zapped into the world of Monster Rancher and meets the girl Holly and the monsters Mochi, Suezo, Golem, Tiger and Hare. Together, they are searching for a way to revive the Phoenix, which is the only monster capable of stopping the evil Moo. (Source: ANN)