Upon entering Serene Walkway, you'll see a Water Elemental Gate to your left. Use a Water Skylander to open the way, and complete the challenge inside to earn this.
After battling the Loose Cannons, you'll be near Magic Elemental Gate. Use a Magic Skylander to open the path, then complete the course inside (it's pretty simple).
When you reunite with the caravan outside of the Security Hutch, cross to the Swap Zone before joining them. Use a character with the Rocket ability to complete the course and earn this.
When you reach Hibernal Harbor, make a left to reach a dual Air/Life Elemental Gate. Use a Swap Force character combination (or two appropriate Skylanders, if you're playing co-op) to open the way, then make your way through the course beyond to earn this hat.