The retreating Eggmobile is a boss from Sonic & Knuckles, as well as its locked-on form, Sonic 3 & Knuckles. It is fought in the second act of Death Egg Zone, after the fight with the Great Eggman Robo. The name for this boss comes from the fact that this is the second time Sonic has to chase after Eggman, the first time being at the end of Labyrinth Zone in Sonic 1.
Sonic has defeated the Great Eggman Robo, but the Death Egg is starting to fall apart. In a last-ditch attempt to keep the precious jewel from Sonic, Eggman takes off in the Eggmobile, carrying the Master Emerald with him. Sonic must hit Eggman eight times, running at top speed not only to catch up with the evil doctor, but to avoid falling off the floor which is rapidly dropping away—nearly as quickly as Sonic can run. If a life is lost, the whole battle has to be done again from the beginning.
This boss is really the third phase of the three-part boss battle that takes place at the end of the Death Egg Zone in Sonic & Knuckles. See page Great Eggman Robo for information on both this and the other phases.