How do you get a metallic egg in sonic adventure 2 battle

Hook up your GameBoy Advance to the GameCube while you have Sonic Adventure 2 Battle running. Go to one of the chao gardens to the machine that looks like a GameBoy Advance; while holding a chao. Then you can send that chao to your GameBoy (it's a requirement.).
[Keep in mind that you don't need a game pak in the GameBoy Advance. Leave it empty.]
Once your chao is transferred to the GameBoy Advance, you can use that chao to play games that earn rings. These rings can be used to BUY METALLIC EGGS on the GameBoy, which can be sent back to Sonic Adventure 2 Battle when you transfer your chao back to the garden. Give it a shot sometime!