Dragon Warrior Monsters 2

From Wikipedia:

Dragon Warrior Monsters 2, known in Japan as Dragon Quest Monsters 2 (ドラゴンクエストモンスターズ Doragon Kuesuto Monsutāzu Tsū), is a video game published by Enix for the Game Boy Color. It is the second Dragon Warrior Monsters game for the Game Boy Color and features two different versions of the same game, Cobi's Journey (released as Dragon Quest Monsters 2: Ruka's Journey in Japan) and Tara's Adventure (released as Dragon Quest Monsters 2: Iru's Adventure in Japan). This was the last Game Boy Color title released in North America that was also compatible with the original Game Boy and enhanced for the Super Game Boy. Both games were remade in 2002 for the PlayStation in a compilation game called Dragon Quest Monsters 1+2 and released only in Japan.

Instead of traveling through portals like in the previous game, the player attains keys that lead to different worlds. The only differences in the two versions, aside from the main character, is that there are different monsters the player can find in the wild and different keys for each game. The game also introduced the new monster family, Water.