Trico will immediately get distracted by that delicious blue smell. Your job is to tolerate it this time since there's not a lot else you can do.
Head back toward the entrance, and you'll find a ladder on your right. There's a chain at the top to open the gate. Trico will float through on the smell like a cartoon character. The gate will close when you let go, but you can just climb through.
On the other side, you have to take a leap of faith, but Trico is right below you.
Climb down off of your obsessed friend, and start pushing the pot of blue liquid. You can try to pull the cart, but the handle will break off. You'll come to a junction in the track that leads you to the right. This track doesn't go anywhere, though. Push/pull the cart back to the bridge that you passed under. Trico will stop there, and you can climb up onto his head and jump to the bridge. Turn left and climb down the ladder to find the switch that controls the track.
With the junction switched, you can push the cart farther along the tracks. This doesn't go well for you.
You'll end up in a water-filled room, but at least that blue liquid is dumped out. Swim over to the platform, and shove the box in the water. Drag the box to the far right corner. Stand on the box and call for Trico. Call a lot. Call for a while. Trico will eventually get sick of listening to you and smash the floor until a hole opens up.
We replayed this puzzle three times and had the same (let's call it a) quirk every time. What's supposed to happen is that Trico's tail drops through the floor and you climb out. What happened all three times we played was Trico broke the floor, his tail got caught in the rafters, the celebratory dialogue played and we stood there dripping and confused. The way we finally got this to work right was by jumping back into the water and swimming away. This got Trico's tail to drop into reach.
Climb up to Trico's back, and he'll jump you up to the next area. Let him smash the suits waiting for you there.
When he's done, climb through the gate. On the other side, there are two crates and a Trico Treat. Push the two crates into a row in front of the hole in the gate. Toss the barrel onto the crates, then climb up and toss it out to Trico.
Climb onto Trico's back, and head out to the domed room at the end of the hall. There's an open window on the left. Ask Trico to stand up against the wall and jump to the window.
Take the ledge to the left, then drop down to the roof of the walkway below you.
Run to the end of the roof, and then drop into the walkway. Turn around and start heading back the way you came, jumping across the gaps in the floor. Back by the door, there's a suit of armor waiting for you. The door is barred, and the suit will grab you before you can unblock it, but Trico won't stand for that.
That doesn't go well for you. The walkway you're in starts to collapse and you have no choice but to run. Just keep running. You'll run out of walkway eventually, but Trico will swoop in to save you (we're not going to count this one, though, since it was his fault).
After saving you from the hallway he knocked down, Trico will toss you onto his back. Ask him to jump to the ledge against the wall behind you on the left. Keep encouraging him to jump to the large platform, then walk inside the building.
This is a large arena. When you hop onto the floor inside, several suits of armor will emerge — including one with a shield. This one is your target. Knock the shield out of his hands, then stay out of reach. Keep knocking down any suit that picks up the shield. Try to knock any suits off balance you can and keep leading any strays back to Trico. After the fight, attend to your friend — remove any spears and give him lots of love.