Hamtaro: Rainbow Rescue (とっとこハム太郎4 にじいろ大行進でちゅ Tottoko Hamtaro 4: Nijiiro Daikoushin Dechu?) is a video game developed by AlphaDream for Game Boy Advance and the sequel to Tottoko Hamutaro: Tomodachi Daisakusen Dechu (Japan only), Hamtaro: Ham-Hams Unite! and Hamtaro: Ham-Ham Heartbreak. It was released in Japan and PAL regions (but was poorly distributed in some countries which makes copies of this game rather rare). It was set to be released in North America, but was cancelled. The series is based on the manga Hamtaro, written by Ritsuko Kawai.
The game involves an extensive plot. One day while playing outside, Bijou witnesses a great rainbow. The rainbow disappears and Prince Bo falls to the ground. The Prince states that he can make rainbows by using his umbrella. He tries to prove it to disbelieving Stan and the rest of the Ham-Hams, but realizes too late that the colors on his umbrella are gone! And thus, Hamtaro and his Ham-Ham friends must set off on a journey in order to collect things that are the proper color for Prince Bo to use for his umbrella so he can create a rainbow to return home.
Certain minigames are needed to reach the colors, and the player must have certain Ham-Hams in their party in order to play them. For example, Sandy is needed to ride pigeons, Bijou is needed to collect falling petals, and Penelope is needed for rolling on top of cans to get across small streams.
In addition to the original Ham-Hams, the game contains some additional characters, most of which were never seen in the English anime. These include Prince Bo, who is the prince of Rainbowland (a castle that is made of clouds); Flora, or Nurse-Ham; Tux; and other various characters.
Source: Wikipedia, "Hamtaro: Rainbow Rescue", available under the CC-BY-SA License.