The fifteenth colossus, Argus, is surprisingly quite easy to find. Just head north along the colonnade. When you reach the area where you dropped down into the pit to fight Celosia, head east across some desert until you see a large stone castle. Dismount Agro and head inside. You'll be in a large arena with two towering walls on either side of you. Head to the back of the arena and Argus will climb over the ledge to greet you.
Argus is one of the largest colossi in the game, a huge giant, with a huge knife to go along with it. The trick to beating him is to get high up to the top of the walls either side of the arena. Lead Argus to the tiles beneath the shortest wall sections on either side. Stand on them, and eventually he'll lift his leg to try and stamp on you. Move out the way quickly, and the tile tilts. You can use it to jump up and grab the ledge. Climb the stairs. Now, pull out your bow and arrow and shoot the furry sections around his shoulders to provoke him. He'll swing his knife at the walls, causing blocks to fall. Climb up these to reach the next tier of the temple. At the very top, there are bridges leading across the arena.
Get onto one of these bridges, but don't go near the middle; stay near the walls. Use an arrow or two to get Argus' attention, and he will break the bridge with his knife. Whilst he's bringing his weapon back, you can jump from the remaining section of bridge to his head, where there's a glowing weak point. You won't necessarily get time to get a fully-charged stab in; Argus shakes a lot. Once the symbol on his head is gone head down to the arm that's holding his knife and you will see blue light on a particular section. Hit that and he will drop his knife, revealing the vital on his hand. Drop down to the ground.
Unfortunately for you, Argus is now even more enraged than before. Instead of attacking you with his knife, since you disarmed him, he will now try and pound you with his fist. Wait until he's about to bring his hand down, and move to one side to avoid it. It's only briefly, but his hand will get stuck in the ground, and you will be able to see the glowing weak point. Quickly jump onto it and hold on. The moment it's relatively stable, charge up a stab. You can finish him off with one hit. Argus will fall, and now, only one more colossus stands in your way.
You will find the final weak point on the left side(your right) of his chest. Jump onto his head and climb down his fur to reach the final point and bring down the Colossus.