Peacock Hat (+10 Armor, +10 Elemental Power, +10 Maximum Health)
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.
Fishbone Hat (+9 Speed, +7 Critical Hit %)
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).
Bearskin Cap (+5 Critical Hit %, +10 Elemental Power, +10 Maximum Health)
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.
Ski Cap (+6 Speed, +30 Maximum Health)
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.