Instructions
Run at the boss. Jump up and slam into its head, just above the spiked weapons it is trying to kill you with. Touching the spiked weapons will remove one life from Sonic, but hitting the head will cause damage to the boss.
Watch for periods when the boss stops moving. You will most likely find it easier to jump and hit it during these periods.
Dodge any projectile attacks that are fired at you. Periodically Robotnik will fire the spiked weapons it is carrying. Dodge these and move in for a hit while it is temporarily defenseless.
Hit the boss a total of 12 times as quickly as you can. After the 12th hit, the boss will die, and the game will be over.