In Northern Ryoshima Coast, you should see an island with a large tower on it. You won't have access until you encounter and befriend Orca, but as soon as you do, you would do well to journey over here first. The island is assailed by the wails of a cat high up on the tower, and the entire island is populated by cats to feed. Once you enter the interior glade, you'll see strange markings on the wall. This will be your cue to jump onto the wall and press the jump button again, allowing you to connect with the wall and continue climbing. Climb the entirety of the tower, taking stops every now and then to feed the cats or claim treasure on the platforms on the way. By the time you reach the very top, a lone cat is crying because it is hungry, so I do hope you manage to bring some Fish with you, or it'll be a long way down just to come back up again for that.
*Note: To get all of the Stray Beads, you "will" have to journey back up this a second time. You can't use the Mermaid Spring to cheat your way up to the top for it, though you can do that if you forget to bring some fish with you to feed the cat at the top.