Morpha has only made a single appearance in the Legend of Zelda Series. It appears as the boss of the Water Temple, the temple that everyone loves to hate, in Ocarina of Time. Morpha is really sort of an abstract sort of boss, as the actual enemy is nothing more than a small spherical "nucleus." The nucleus itself cannot do any damage whatsoever, but the nucleus has the power to control any body of water that it dwells within. The arena in which you battle Morpha consists of 4 platforms in the middle and a surrounding platform (the walls are lined with spikes here). The rest of the arena is a body of water that Morpha posseses complete control over.
Battling Morpha is painfully simple. However, Morpha can deal out tons of damage (about 3 hearts in one attack), and people often use strategies that simply don't work against it. Because of this, many people claim this boss to be one of the hardest in all of Ocarina of Time. These people are mistaken. There are several strategies that are very effective in killing Morpha, and the best part is that you will most likely take no damage at all.
The most important thing to know about Morpha is that being in the water is hell. Do not enter the water under any circumstances. That being said, being surrounded by water sucks too, so don't use the middle 4 platforms if you can avoid it. So that means that you should be spending the majority of your time on the outside platform. Once you are on the platform, stand patiently away from the water for Morpha to form a water tentacle. It'll begin to stretch out on the platform, and at this time it would be smart to move down either side of your platform, within range of the Longshot, however. Once the tentacle has been out long enough, Morpha's nucleus will be at the tip of the tentacle. Use your longshot to pull it out of the water. As the nucleus attempts to hop back to the water, take the opportunity to slash away with your Master Sword (or better yet, BIggoron's Sword). By repeating a few times, Morpha will die rather quickly. Take note that as Morpha weakens, it will use two water tentacles instead of just one. The same strategy applies here though, just stay out of its range and you'll be fine.
Most of the strategies above still apply here, except you should be standing in a corner of the stage. Once you can, drag morpha out of its tentacle. Instead of going straight to the sword fighting, continue to hookshot it towards you, until you can trap the nucleus into the corner. Then proceed to slash it. By trapping it in the corner, it is unable to return to the water, and will go down rather quickly.