Sir Galleth Cooper is inside the circus tent with the opening on top, but you need to find a way up to that point. Bentley suggests checking out the nearby tower, so use the spires to climb upwards, waiting for the blue ball thing to swing around so you can grab onto the rope. Jump off on the platform with a barrel full of arrows to get an introduction to the Archery Costume.
Follow the instructions given to fire an arrow at the target in the distance. Note that if you hit the bullseye of any target, you will get some coins. Use the ropes to get inside the tent. This part of the mission should be familiar to you with the first public demo. Use the Archer Costume to get a rope across and use it to get to the next area.
Once you get to the next platform with arrows, shoot it at the target and the rings will start shooting out flames. Time it to make it past them without getting burnt, then continue along until you come to some trumpets. If you stand on these for too long, then they fall with you on it. The next target is moving side to side, so don't worry about getting a bullseye. Break the objects on the next platform to reveal another barrel, which you can shoot to the target hidden behind a breakable barrel, which leads to a platform with a Secret Sly Mask.
Use the trapeze swings to continue farther, then jump on the catapult to the next arrow barrel. When you hit the next target, a bunch of cannonballs will be firing at you while you cross the rope; these aren't hard to avoid. The next target is slightly difficult to hit straight on, so guide the arrow to either side a little bit to bypass the cannonballs. There's more trapeze swings, then more trumpets. When you get to the rope to climb up, do so all the way up to find another Secret Sly Mask.
Jump off on the platform, then slide down the rope when the fire stops. The last target is swinging around in a circle, so hit it and then walk across. The rest of the path to Sir Galleth is easy, so another mission complete.