A Yule woman would like nothing more than to get her hands on a snazzy swimsuit.
This errand is available to complete after defeating Cap'n Crossbones and arriving at Yule.
In Yule, there's a woman walking around in circles around town; talk to her to find out that she wants a swimsuit from Castaway Cove. Simple enough; use Travel to go there, then talk to the woman from earlier, whom you helped design a new swimsuit. (She's the one walking around in purple pants.)
Of course, as chance would have it, her very last one was stolen, so you must retrieve it. Go back out on the World Map and summon Tengri, then go west to the island of Bungler's Bay. Land on the northern part of the island just below some trees, then seek out the treacherous seagull to your east. Use Nature's Tongue to obtain the snazzy swimsuit. With it in hand, return to Yule and give it to the woman to complete the errand.