This new area is apparently the beast's lair, The Nest, and Trico definitely wants to go up.
Turn right and look for a tiny ledge that leads back along a tunnel.
Use the ledges and the hanging chains to make your way all the way to the back of the tunnel. Use your mirror to convince Trico to attack the wooden wall across from you.
Destroying the wall knocks down a pillar — run down it and then turn left. Head up the stairs you find there, then go through one of the windows you see on your right.
Trico gets his head stuck in the most adorable way ever, so you're going to have to figure out how to get him through here.
Go up the stairs on the right side of the courtyard you're in. Turn right at the top and keep going up. You'll end up on a balcony over the chasm you just crossed. Call to Trico from here.
Once you get Trico into the hallway, use his lightning to uncover a Trico Treat™ (we've decided to call them Trico Treats, but that's not cannon).
Get back to the courtyard. Trico will lay down in the sun and you can climb onto him to get at some ledges on the left side. Climb up and edge along the ledges to the right toward the hanging chain. Climb the chain up, then turn left to find another large tunnel.
Trico will jump up and follow you in. There's a tunnel on the left where you can find another Trico Treat. Feed him, then go back to the main hallway. Use your mirror to target the wooden wall ahead of you.
Run through the opening and you'll soon find another wall blocking your progress. Crawl into the crack to the right to get past. Trico will hop up and over to join you on the other side.
Follow the wall on your right down toward the cliff edge, then go around it and head back up. Climb on Trico's back and he'll hop over the wall again.
Trico will freeze when he walks into the next area. That eyeball stained-glass thing is freaking him out. Climb down and push it off the edge to calm him down.
Go up the stairs ahead of you and through the crack you see on the right. Retrieve the Trico Treat and bring it back to him. Turn left and head up the stairs — Trico will follow you.
When you get to the next room, climb onto Trico and jump to the ledge above you. Head through the window in the middle.
This will lead you to some ledges. There's no trick here — just climb up and down as you need to to continue along. Your goal is small tunnel that will let you into the room to the left of the one you started in. It's just a little ways down the path.
Drop down once you're inside and pull the lever to open the gate on your left, allowing Trico inside with you. On the right, you'll find another Trico Treat in the ground. Pull it up and feed him.
Directly across from where you came in, there's another hallway blocked by a wooden wall. Do the mirror trick to destroy it.
There's a weird, evil-looking birdcage in the next room and Trico freaks out a little. Climb down and call him to get him to come anyway. It doesn't end well.