When you defeat the Waterwraith, go to your Piklopidia. Go to his entry and listen for awhile. You will hear it singing.

When in the submerged castle, dodge the Waterwraith until you get to the final sub-level 5. You will have to get the Purple Pikmin and take only them to the eggs to power them up. Then, break down the door to the big circle area. Let him fall. Wait until he moves then put Olimar in a safe area. Use the President to fight. When it is moving, throw the Purple Pikmin on him and he will freeze. Then, just keep throwing them. When he falls off his wheels you will have to chase him and make him tired. Then, throw the Pikmin again. Keep doing this to defeat him.