Skyward Saga of Kain

"The aerial fantasy story of a boy that soar through the skies and hunt beasts." Humanity has abandoned the earth and now lives in giant islands in the sky. The main character, Nina, hunts sky beasts with her talking cat, Cake. The defeated beasts turn into sky gems which are highly valuable items. Though when the ship she's on is destroyed by a massive sky beast it leads them to an unknown island with many mysteries.