From where Trico finally lands safely, head back inside along the hall behind you. Continue along the hallways until you come to a room with another stained glass eye.
This means that Trico won't follow you inside, which is bad because there's a suit of armor below you. You can just run past him, though, and up the ramp in the back left corner, then climb up the ledges to the platform. His spell-like things might start to pile up around your screen if you take too long. If they become a problem, mash some buttons to try to clear them away.
Right by where you climb up, there'll be a chain hanging down. You're not going to climb up this one, though. Instead, grab it, get a running start and use it like a zip line to cross to the bridge with the eye.
Once you get there, shove the cart off and let Trico come in to take out the suit of armor. Follow the rails out of the room, and then take the left fork.
This will lead to a ladder you can take down and then a switch that will open the gate, letting Trico out. Head down the hall to the right of the switch.
Once again, a stained glass eye block Trico's path. This one is suspended from a giant mobile, so it's a little harder to get to. (This type of art installation/baby toy, by the way, is pronounced like the city in Alabama and not like the phone which means that I was right and my girlfriend was wrong when she corrected me and I've published that now so it's irrefutable.)
Climb up on Trico's back, and ask him to stand to get up to the walkway above you on your left. Toss down the two Trico Treats you find there to keep him occupied while you wander.
At the end of the walkway, there's a gap in the railing on the left. Jump out onto the disc, then to the cage.
From the top of the cage, jump to the chain hanging to the left of the second disc. Slide all the way down the chain until you can drop onto the wooden planks below.
The planks are balanced in the middle and are currently too low for you to reach the dangling ladder-thing hanging off the eye. Stay on this end of the planks until your weight tips the other end up, then run and jump onto the dangling thing.
Climb up to the eye. Make your way around to the front and stand on the ledge. From here, you can climb up and pass to the other side of the eye.
Drop from here to the bottom ledge again. Work your way across the eye to the right, mirroring what you did before. Climb up to the ledge above you, then up again and pass through the eye to the front side.
Use the ledge to get to about the center of the eye, and climb onto the top. Climb up the rope from here (this one doesn't have one of those spiked squirrel guards on it).
When you reach the mobile arm at the top, jump across the the planet-looking object and climb its chain.
Walk along the arm at the top the chain, and climb up again. Repeat this a few more times until you reach the very top of the mobile.
In the center of the walkway, you'll find a switch that will detach the entire mobile (that's the last time we'll get to say mobile, which is sad because, and this is important, I was right) and send it plummeting.
Trico will hop onto a pillar underneath the far end of the walkway you're on. Jump down to your friend.
Get Trico to start jumping along the pillars. He'll stop on a wooden scaffold because there's another stained glass eye for you to shove off.
Climb back on board, and get Trico to climb the pillars up. You'll run out of pillars across from a closed drawbridge. We'll get that open in the next section.