This is a particularly annoying achievement that is based far more around luck than skill. Be prepared to put in a fair amount of hours attempting this, perhaps try half an hour or an hour every now and then.
You should be attempting this on level 1-1 only. To clear a level you need to fill the meter in the top right of the screen (which stops the balls from generating) and then clear all the remaining balls. The best way to fill the meter is chaining combos, that is given a sequence like this:
[red] [red] [yellow] [yellow] [red]
Firing a yellow ball into the middle will cause the yellows to clear and the reds will drag back together and clear as well, thus causing a chain. Each consecutive chain causes the meter to fill by a larger amount. Other good ways to fill the meter (in normal play) are gap shots and hitting the coins. However, you won't have time for that trying for this achievement. You should be looking to shoot a ball that will cause as big a chain sequence as possible. This will fill the meter and if you get it right will actually drag some of the balls back inside the spawn meaning you won't need to clear them with additional shots.
Bear in mind that you can only really afford to shoot two balls in total here. Any more than that and it isn't likely to work as your very first shot needs to start off this continuous chain sequence and any pause can stop them from being dragged backwards. There really is zero margin for error.
Your first shot is going to need to be roughly straight down (around the six o' clock position) and the second will be towards the upper right (between the one and two o' clock position). You may have time to swap the two balls you start with but in general I didn't bother, I just restarted instead. In fact, quite often I didn't even end up firing a single shot - you can see straightaway if there is nowhere for the first ball to go towards the bottom of the screen.
Thanks to IQwz
we finally have a video: