In the first part, the key to defeating Mordroc is to use the "green arrow" that is located in your inventory (press Start). Select the green arrow and lock on to Mordroc. Fire the bow with the green arrow five more times. You have to replenish your green arrow one at a time by killing the mini-black dragons that Mordroc fires at you. Keep collecting the green arrows and make sure to lock on to Mordroc.
In the second part, once Mordroc goes down upon his knees, he changes into a Black Singe. All of your elements are taken by Mordroc and you are going to have to fight the old-fashioned way. He flies around shooting lightning bolts from his mouth. Run away every time you see the electricity forming around his mouth. Get into your guard stance when you do not see the electric bolts forming around his mouth. In another words, Mordroc the Dragon shoots out a ball of electricity (instead of the stream of electricity), and you have to catch it by being in your guard stance. Once your sword catches the bolt, release the bolt and use it against Mordroc. Once Mordroc the Dragon falls to the ground, run up to him and strike his stomach with the sword. The process then repeats. Remember to keep a close eye on his mouth -- electricity forming around the mouth is bad and no electricity around the mouth is good. Do this five times and enjoy the ending sequence.