The Egg Ball is the third boss in Sonic Advance, which takes place in Casino Paradise Zone. This boss consists of an Egg Mobile and a spikeball. These two spherical objects appear from one of 8 pipes and you must avoid the spikeball while hitting the Eggpod; a total of eight hits, or six if in easy mode. The speed of the two balls will increase as Eggman is hit.
Amy & Knuckles both have a much easier time with this boss than Sonic & Tails. Simply ducking between the two pipes on the bottom of the screen will provide you with an area that you cannot be hit in. Then, you need only wait for Eggman to come out of one of the vertical pipes or the lower horizontal one & hit him with their standard attack (for Knuckles it's the three-punch combo, & for Amy it's her hammer smack).