Shadow of the Colossus/Phaedra - Colossus 4

Ride Agro down the path into the valley. Though he will be available for this fight, he is essentially useless. You'll notice a set of four openings arranged in a square when first entering this "arena." These will be key in defeating this colossus. Moving a little further down will start the cutscene that shows the fourth colossus awakening and ultimately begin the battle. Say hello to Phaedra, the War Horse.

Immediately turn around and sprint for the caves. Jump down into one and wait near the entrance. Unlike the others so far, Phaedra requires an element of stealth (or simply cowardice) to defeat. You'll know that he's above you when the ground really starts to tremor (it may even knock the hero off his feet) and dust falls from the ceiling. Once you're sure he is above you, there two options for how to proceed. The first is to simply wait in that spot until Phaedra lowers its head (you'll know its coming when the tremors stop. When it does so, you'll see a pair of (what look like) long dangling earings, which you can grab onto if you run and jump. From here, simply jump-climb your way up to the top of its head, where the weakpoint lies. As usual, charge-stab until he falls. The problem with this strategy is that climbing up Phaedra's earings wastes a lot of stamina, so the probability of falling off his head increases. He tries to knock you off a LOT, so beginners should probably try the second strategy.

This other technique involves coming up behind Phaedra while he's thrashing about above the cave you orginally jumped in. Run around in the cave and come of the opposite side from the one you entered. If you've done this right, he won't notice you. Next, run towards his flank and you will notice that his tail is fairly close to the ground, thanks in part to the elevation. Jump and climb up this onto his back. this is a good place to rest and recover stamina. Once you're ready, go to the base of Phaedra's neck and poke the mini-weakpoint (similar to the point on the first colossus' ankle). He'll lower his neck and you can climb atop his head and defeat him with a few quick blows to the head.

Hard Mode Strategy
You'll still need to get on Phaedra's head eventually, but start off by climbing atop his back from behind. On the shoulder area on both of his front legs are two magical weakpoints for you to take care of. Charge-stab both of these to take out the first half of Phaedra's life; you should probably rest between each shoulder attempt. Once they are both taken care of, proceed to the head by way of the neck weakpoint and finish him off.