Shadow of the Colossus/Quadratus - Colossus 2

The second colossus you are guided towards is Quadratus, the Bull. It is as large and lumbering as the first colossus and can be found by crossing a natural bridge directly north of the Shrine of Worship. You will need to follow a path down towards the beach once the bridge is crossed an approach the sealed off cave before the colossus will reveal itself.

After the short cut scene, it's time to prep for battle with the beast. Start by riding (if you're still on Agro) a good distance away from the colossus. From there, switch out the hero's sword with his bow, then dismount and slowly approach the beast. It is a good idea to remain cautious with your distance as being step on will lower your health.

The colossus' first weak point is on the bottom of it's hooves. There are a couple of strategies that can be used to attack them. The first and probably simplest is to wait for the colossus to rear on its hind legs when about to stomp on the hero, and then fire an arrow at the glowing bottoms. Another technique involves flanking the beast and firing at the back hooves while it walks. Each time it moves its feet, the yellow undersides are briefly revealed. You will need to have proficiency with the bow for aiming and timing. While doable, this technique is by far more difficult.

Regardless of your method, the colossus will fall to its knees. Take this opportunity to climb up the hairy upper-regions of its front legs and onto the colossus' back. Your goal from here is to reach its head, where the colossus' first magic weak point lies. Getting there can be a little tricky with the beast's bones sticking out of its skin, but this can easily be overcome by running alone the spinal cord. Be careful because Quadratus will likely try to shake you off. If this happens, you can always jump onto the furry portion of his back and hold on until he's done.

So you've reached Quadratus' head. Now simply charge the hero's sword and stab it like you did with Valus. It may thrash its head a bit, but as long as you hold on there should be no problem staying on. After about half his life is drained, the magic weak point will vanish. That's right, Quadratus has more than one weak point. From this point on, there are very few colossi that only have one magic weak spot (most have two or three).

Don't worry though, the final weak point is located at the opposite end of his body. Simply run along the spinal cord towards his tail, crouch down once the magic symbol is reached, and stab like before. After a few successive stabs, Quadratus will fall and the hero will be transported back to the shrine for his next assignment.

Hard Mode Strategy
Once the mark on the Quadratus' flank vanishes, hold up the sword. The weakspot will appear on one of furry sides used to climb up it. If the points gather at the left, head towards his left side (and vice versa). Now climb down until you see his weakspot and finish the beast off once and for all. If you fall off from fatigue (or another reason), shoot one of his hooves again and climb back up.