In the Tea Cup Court alley, there is a mini game called Court King. This game requires you to shoot basketballs into a hoop for 60 seconds. The achievement pretty much speaks for itself. To get it you have to sink a basket in the last remaining second of the 60.
I'd advise you to play the game as normal until there are about 5 or 6 seconds left on the clock. You will then have time to watch the counter countdown to 1 and then release your shot. During the first 50 or so seconds try and find a throwing position whereby you are getting most of your throws in the basket. It does seem to be a little temperamental where it doesn't seem you move in between shots yet the ball seems to fly off in a different direction.