Death Egg Robot is the name of a boss in Sonic Generations. The boss arena is the Death Egg from Sonic 2. The battle is played by Classic Sonic.
The battle only takes 4 hits to defeat. 2 on the platform is get behind him when he launches his arm at you. The last 2 hits is when you unleash a mine, then he hits the mine, then you Spin Jump on him. Then the battle is won.