When Trico delivers you to the next area for you to explore, he'll start batting at a chain.
You can't quite get onto it from the ground (and Trico's playfulness doesn't help matters), so climb onto his head so it's easier to reach. Climb the chain, and jump to the wooden staircase.
Follow the staircase up and throw the switch you find on the other side. This will light a pillar and Trico will jump up onto it.
Work your way back around and jump onto Trico's tail. Climb up his back and jump to the ledge on the right. Follow the path left and up the stairs.
Jump to the planet-looking thing in front of you when you come through the door. From there, jump onto the cage to the right. This will bring you within jumping distance of the wooden planks on the wall. Jump across to grab them, then drop down. Hang off the edge of the platform you land on, and descend the chain.
Jump off when you reach the bottom, and go throw the switch. This will lower the pot of liquid Trico Treat into a basket on the left. Go retrieve it.
Carry the pot up the stairs. At the top, you'll come to a couple of doors that are barred — you saw these from the other side earlier. Set down the pot and unbar one or both of the doors.
Carry the pot through and work you way down to the ground (it's okay to just toss the pot so your hands are free). Take the pot back to that chain you first climbed and hang the pot on it.
This is a perfect Trico toy, it seems. He'll grab the pot and start pulling. This will open the gate enough for you to run through.
On the other side of the gate, there's an axle and a ramp on your right. Push the axle up the ramp and into the metal cradle at the top. Go around to the end and push the axle out of the cradle to stand it up. Get down to the ground and push the axle over to the gate. Wait for Trico to grab the chain again, and shove the axle under the gate to prop it open for him.
In the back of the room, you'll find another Trico Treat. Feed him, then climb onto his back.
Urge Trico into the hall ahead of and above you. He'll go along a little ways, then get stopped by a pair of those stained glass eyes. To the left of where Trico stops, you'll find the helmet from a suit of armor. Carry it over in front of the one of the eyes and throw it. Repeat the process on the other side.
Head down the stairs in front of you until you come to more of those stained glass eyes. This next part is pretty intense, so we'll pick it up in the next section.