Play as Kiddy. When Kaos stops and his blades start to rotate, press A to put Dixie on Kiddy's shoulders and jump from blade to blade. At the exact moment after you hit Kaos in the middle of his head, continuously throw Dixie up into the air and move back enough so that she will land back on Kiddy repeatedly. If done incorrectly, bouncing off Kaos' head will send you too far from his head, and bring you to the floor. Otherwise, you will defeat him, but not completely, as he leaves and you will not see him again until you enter K. Rool's lab. If you have a controller with a turbo feature, you should not have any problems throwing Dixie continuously. You will not have to wait for him to move back and forth, or shoot you. If you hit him only two times then fall to the floor, you still have to wait the total amount of time for him to go back and forth the total number of times he does after the first two times you hit him and fall to the floor. With three or more hits, you will just have to avoid getting shot before trying again to hit him.