Battery Life

This will depend on the console you are using and the upgrades you have.

Game Boy Color

Since the GBC uses the same battery as a Game Boy Advance, you can expect the same life expetency as seen in this article in the GBA section.

Game Boy Pocket

The GBP has less of a power supply than the other consoles. You can expect around 2 to 3 hours on a console that is modded with an IPS kit and other mods that draw power. Use of an EZ-Flash or similar, will significantly reduce the battery life.