Puma Hat (+10 Armor, +2 Critical Hit %, +10 Elemental Power)
From the start of the zone, turn around and take the path leading away from Rufus. At the end of this short path is a cleverly hidden hat.
Turkey Hat (+50 Maximum Health)
Climb the Mushroom Stairway in the center of the hub world. When you reach Treetrunk Peak, move out onto the branch and use the launch pad. You'll be sent into the pool below, teleporting you to a secret platforming level. Make your way across the platforms to receive this hat.
Stovepipe Hat (+5 Armor, +2 Critical Hit %, +5 Elemental Power)
Fairly early in the level, you'll be introduced to Elemental Gates. The one presented to you is for a Life Skylander, so use one to open the path. Free the caged sheep and take out the Greebles beyond to receive this.
Greeble Hat (+20 Maximum Health)
In Tangled Thicket, you'll reach the game's first Swap Zone. Use a character with the Rocket ability to activate it. Fly through the obstacle course to receive another hat as a reward.
Glittering Tiara (+6 Speed, +2 Critical Hit %, +10 Maximum Health)
Upon exiting Shadow Spelunk, you'll be met with an Undead Elemental Gate. Use an Undead Skylander to open the way, and you'll learn that some Evilized Greebles stole Skully's top hat. Follow the path to battle the Greebles and retrieve the hat, then return to Skully for a hat of your own.
Boater Hat (+3 Speed, +20 Maximum Health)
When you reach Froghollow Fishin' Pond, look west for a path that extends around the water. Follow it to reach a Swap Zone. Use a Swap Force character with the Rocket ability, and complete the obstacle course for this reward.