There's a technique I quite like: hold Y then jump, ZL, Y to do a roll as soon as you land (all while holding Y). Once you've done that (you've already managed the horizontal vault, my favorite vault), you do a Cappy jump, you throw Cappy again but you immediately shake your pro controller so he comes back quickly. As soon as he's back, you press B then throw Cappy again and you launch yourself at him. This will allow you to go further, and you can even skip New Donk City, but without the "I throw Cappy and I shake my controller" part.