As the name states, Egg Press is actually a large spring hooked onto an Egg Mobile similar to the Bouncy Boss Robot from Sonic Chaos. The Egg Mobile is orange with some black and yellow stripes on it. The spring is gray.
Dr. Eggman starts off the battle by trying to squish the player as he's jumping toward them. After several hits he'll jump high off-screen and the player must dodge him by basically running around. The impact of the landing also creates an invisible shockwave which will damage the player if he/she remains on the ground. He'll do this after another couple of hits as well.