While the Hard Boiled Heavy robot, Heavy Gunner is the technical boss of this stage in the Studiopolis Zone, I actually thought I was fighting just the helicopter in this one until I was pointed out the robot trying to kill our favorite blue hedgehog.
The stage moves pretty fast and the key is timing here. Red missiles are bad and blue missiles when jumped on will send it right back to its master and that's how you defeat him.
This was the first boss to give me some trouble, I died a few times against him. But once I mastered the jumping, it was fairly easy.