Dark Carvo will first make two Bosses that you have defeated in the past.
Do not try to attack them; just try to dodge them. Once they disappear, you will have a chance to attack Dark Carvo. He will make duplicates of himself and try to attack you. Try to dodge him. He will lose you and stop trying to find you. This is your chance to attack him. Grab an egg and keep attacking the Dark Carvo. Once you find the real one, he will get weak and you will have another chance to attack him. Repeat these steps to defeat Dark Raven.
Sonic Team eggs:
Get the indicated number of coins to unlock a Sonic Team game character egg.