Released June 2001, Silver Beast Machine God Liger Zero (白銀の獣機神 ライガーゼロ) is the only Zoids game made exclusively for the Game Boy Color. Unlike Genobreaker Storythingy, it wasn't packaged with a limited Zoid, though I have heard the first run came with a gashapon Zero repainted silver. It also tells an entirely unique story with its own set of characters—there's no anime dudes, no crossovers, and no war...and the one tournament battle is a bonus extra at the end where you fight your friends for fun and cash.
Pity it was never translated and released stateside. Even a Legacy-style rush job would have been fantastic. But it was far too old and far too anime-unrelated, most likely.
If you still want to play (and want an actual cart), Silver Zero is easily found used on eBay or Amazon.co.jp with a little patience. There's also two versions of the ROM out there, one original and one that sometimes claims to be translated. The only thing that's done are the menus, alas.
Try this walkthrough on GameFAQs if you need a guide. Another review (in Japanese) can be found here at Zoids World.