At the beggining of the duel, the large Migen will punch downward at you. You can grab upwrd, and catch his fist. Once you have his fist, you can throw it at the large Migen, but the smaller one will heal him before you can defeat him, so it's not worth the effort. Instead, throw his fist at the smaller one.
He'll spit fire after you hit the small Migen; you can grab it to get a blue gem. When you catch his next fist, toss it at the smaller Migen a second time; Now the small Migen will throw an energy blast, and the larger one will spit more fire. Catch both, and send the final punch at the small Migen. Now, with the small Migen gone, the large one will do a fire breathe attack. Just jump and boost, to the side of it until it's done. Now you're ready to take the guy down! He will mix up throwing punches, and fire - And note, punches come from the side now, as well. You can't catch these punches, but you should still block them.
When he gets a baffled look on his face, you can catch his next punch, and throw it up at his face. Continue this pattern until you beat him. (He will begin going faster, howeever.) Also, be aware for his fake punches, where he won't actually punch at all - Just attempt to fake you out.
If you can beat both Migens, without taking any damage, you'll be awarded with a yellow gem.