The easiest way to complete challenge mode is to choose Donatello, since he has long reach. When you are facing such characters as Dr. Stockman, his jumping attack ability will take off a chunk of damage. After that, you face Shredder. Save a lot of shruriken. Throw fire/electric/ice shruriken at him until he dies. You will now face Oraki Saki. Do the same thing (if you have any shuriken remaining), or try to hit him with distant attacks. Also try to get combos on him. After you defeat him, you will face Hamato Yoshi. He has the same attacks as Oraki Saki, so basically do the same thing. After you defeat him, you will complete challenge mode and unlock Hamato Yoshi in versus mode.