She either jumped or managed to climb up with no claws somehow. Cats do jump really high, one time one of my cats jumped all the way to a high shelf. I have no idea how she did it, but cats are very excellent at jumping.
I believe she used her ninja skills and cat-reflexes to, somehow, jump up onto the tree as they crash through the fence. The image below shows that she's just pulling herself up without the aid of claws, as her paws don't appear to be digging into the tree.
posted over a year ago
Now as for the leash and its apparent power to move through solid objects on occasion, well, you'd just have to ask the animators that question...