Shadow of the Colossus/Celosia - Colossus 11
 Finding Celosia
Celosia is an easy find. Head north along the colonnade until you're almost at the top of the map. Just a shade to your right you should see a large pit with a path cut into the side leading down to a small lake. Look for the ruined doorway to find the entrance to the path. Then head up the hill into a temple. Celosia will appear above and behind you as soon as you jump across to the main room.
 Defeating Celosia
Celosia is very different from the other Colossi you've fought so far. Whereas the others were huge and lumbering, Celosia is relatively small and very fast. She is the smallest colossi in the game, and resembles a boar. However, she does possess razor-sharp talons and two scimitar-like tusks, which she'll put to good use during the battle.
This colossus may be small, but Celosia is no slouch. She's very fast, so if you're not paying attention or taking cover she can destroy you rather quickly. Immediately run towards one of the two closest fire altars and hide between them and the wall. Celosia will try to swipe at you from outside, which can be very damaging if it hits. To move the battle forward, notice the ridges on the side of the altar; use these to grab on to and climb up using the jump-climb method. Celosia will switch his tactics to ramming the altar with his forehead, a move that can knock you back on the ground. To avoid this, jump up whenever he gets close with her charge (you'll avoid his impact altogether this way). After doing this once, a flaming stick will fly out of the fire pit and onto the ground.
There's no easy way to do this next part. Unequip your weapons (so that only the hand icon is displayed) and jump off the altar to grab the stick. Press R1 when close to pick it up for use as a weapon. Run immediately to the next altar down and hide behind it. If your lucky, you can do all this without Celosia charging at you; however, if you weren't so blessed, just hope for the best and try to find some cover as quickly as possible. Climb up the altar as you did before, and strike the cauldron with your piece of wood setting it on fire.
Celosia is afraid of fire, so jump down and use the flame of the stick to direct her to the back of the room. If the flame goes out, run to the nearest altar, climb up, and swing at the flame to light it once more. You'll want to direct her towards the ledge facing the small lake outside the temple. Don't rush too much, however, for Celosia will swipe at you if you get too close, which will knock you over and (potentially) put out your flaming stick. Eventually, you'll force her off the edge and onto the ground below, destroying the armor and revealing her back and the vital. Make haste and jump down after her. She'll be stunned for a short time, just enough for you to reach her and quickly climb onto her back. Now just hold on tight - she will take both of you back to the temple, trying to shake you off all the way. Don't bother trying to stab her for now, since she'll never really give you a chance. About the time you reach the gap, your stamina will be low, so let go when she leaps across and recover it.
When you're ready, leap across yourself and ascend the altars once more. This time, when Celosia charges at the altar, jump towards her and grab onto her back. She's not nearly as violent this time, so it should be easy to get in a few, fully-charged stabs while riding her. Once at this stage, she should go down rather quickly.
 Alternate strategy
There is also another option for defeating Celosia that requires less time and stamina. After using the torch to back the colossus off of the cliff, she will lay stunned at the bottom for a short period of time. Equip your bow and carefully lean over the side of the ledge, and shoot her with an arrow. After hitting her she will get back to her feet and run back up to the temple. Use this time to climb back onto one of the fire pillars. When she gets back to the temple, she will immediately target the player and rush the pyre like before. Use the same jumping tactic to avoid being thrown off of the pyre and Celosia should be momentarily stunned by the impact allowing you to drop down onto her back with very little difficulty. From there proceed to attack the weak point on her back until the colossus finally falls. This tactic is most effective in Time Attack Mode as it negates the possibility of the player falling off of Celosia's back as she runs back up to the temple.
Note: If the player should fall or jump off of the cliff down to Celosia and happens to miss her back, there is a chance of losing a significant portion of health and the colossus will awaken almost as soon as you make impact. If the player fails to climb onto her back before she recovers, she will immediately begin charge attacks that when hit, can leave the Wanderer stunned and at her mercy. This particular attack can also push the player far from the temple and out towards the lake if you aren't careful. Due to her fast speed and aggressive nature it will be impossible to outrun her back to the temple and it can be difficult to climb onto her once she's fully awake. She tends to stay very close to the player making it hard to outmaneuver her and reach a point that would allow the player to jump down onto her back.
 Time Attack Strategy
Celosia is a relatively easy time trial because there really isn't much else to do other than avoid wasting time. As before, immediately run over and hide near one of the altars. Climb up and let Celosia ram into it, dislodging the wood fragment. Go ahead and let Celosia ram you a second time just to give you the full amount of her recovery time, jump down and quickly grab the wood fragment and run to the next altar. The rest of the battle proceeds as before. Once Celosia has been injured, shoot an arrow down at her from the edge of the temple and climb the altar again so you can jump back on her back.