At North Ryoshima Coast, go to the island with Catcall Tower on it, then enter the island's inside grounds through the entrance in the thick circle of trees lining the island's perimeter. Once inside, Amaterasu will encounter a new type of demon, the Poltergeist. After killing it, Issun will notice trails of golden pawprints on Catcall Tower. Ignore these pawprints as of now, and go to explore the island's surrounding ground. Dig up and bloom the clovers near the small towers and if Amaterasu has enough Fish Feedbags, feed the cats nearby. After these are done, approach Catcall Tower and jump onto it, pressing jump again as Amaterasu makes contact with the pawprint-covered surface. Jump off the surface to get higher, then stick back onto it. Keep scaling like this up the tower. On the way up, there would be red rings on the tower that generates a golden cloud when crossed. This cloud is solid an can be walked on, which serves as a "safety checkpoint". Each of these clouds mark a floor, with a small platform on the cloud that has either cats, a treasure chest, or both. Note that the eight floor has no protective cloud, but its platform has Stray Bead #67, so remember to constantly circle around the tower as Amaterasu scales her way up, and hopefully catch the eighth floor in sight.
At the top of the climb is a room with a Mermaid Coin and a Mermaid spring. If Amaterasu has run out of Fish Feedbags, then use the Mermaid Spring to warp to the mainland and buy one bag from a Merchant. In the room is a flight of staircase, leading to the top of the tower. There are several intervals on the staircase, which are floors with treasure chests. Reaching the top, Amaterasu is led to the corridor outside of Catcall Tower's top, with a narrow platform and a cat on it. Feed it with a Fish Feedbag, and a constellation will appear. Completing it, Amaterasu will be greeted by Kabegami, who grants her Catwalk. Use it on the Kabegami statue on the corridor, and reach the apex of Catcall Tower, with a large statue of a cat on it. There is another narrow platform behind the statue, and on it is a Sun Fragment. Take it, then jump down to the ground below (there are no invisible walls surrounding this small platform). Once below, use Catwalk on the small towers surrounding the main tower's base, and obtain the treasures and items on them. Leave Catcall Tower, and ride Orca back to North Ryoshima Coast.