Monster Rancher (2000)

Monster Farm: Legend e no Michi

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. Continuing from where the original story left off, Genki and friends journey to conquer the legend cup in hopes of freeing Holly's father from the mystery disc. (Source: AniDB)