The Green Grove Zone boss involves Robotnik using a claw attached to his Eggmobile to drop a spiked ball onto Sonic. He will drop it and the ball will bounce five times toward Sonic. On the fifth bounce, the ball will stop and Robotnik will go down to grab the ball. This is the time to hit him. After he grabs it the cycle repeats. It takes 5 hits to knock Robotnik out.
This battle is considerably easier if you keep the ball bouncing in the middle of the arena, where the ground is lowest, and using the higher ground to hit Robotnik.