Cats have very active nervous systems. They are sensitive to bullet velocity. Anything that goes over 2500 fps and sheds energy quickly will work well. A good deer calibre with soft point, frangible bullets will work. I believe Harry Selby used a .243 on leopard with much success (over 100 happy and uninjured clients). A .308 with 150 grain Hornady round nose bullets would work wonders. It will be a short range shot. Use a bright, low powered scope.