Prerequisites: Complete Back to the Sea, give Leano a Moon Brooch
Reward: None
Unlocks: Dating with Leano
Ahh, sweet romance. Once you've completed the first three quests of Leano's friendship line you can move things to a new level. In order to romance Leano you need to get a Moon Brooch from Silky Stitch Tailor's, which will unlock once you've moved at least one character in the game into dating distance. Moon Brooches cost five Moon Cloves, so hopefully you've been storing them up for a rainy day.
Give Leano a Moon Brooch - and agree that this is what you want - and she'll explain that in order for two pirates to tie the knot, one of them needs to catch a Flying Dragon Fish. She also explains that the Flying Dragon Fish can't be caught in any normal places, so... good luck?
Head to Glaze Iceberg once you have the Advanced Fishing Rod, and bring along a bucket of Hyper Worms. (As of this writing you need Super Worms rather than Hyper Worms. This is doubtless a bug that will be fixed soon.) Head north from the cable car to find Glaze Grotto, a cave with a fishing spot in the middle. You'll see a cut scene involving a conspicuous shadow...
D'aww, how cute.