We’re looking for the treasure that Gau offered us. And no, it is not the Potion. Gau doesn’t remember where it is, though. Go north to watch a scene, then west onto the ledge; Gau will find the Potion there.
Go northeast (but not onto the small ledge, unless you want a negative-500 Gil). Go to the northeast and along the path to the east side. Step on some tile here to trigger the event where we find the "shiny shiny" – a diving helmet. "A" is right. Apparently, when you three jump into the Serpent Trench, you’re all sharing one helmet. Ouch.