This game will backlog your button presses, throwing you wildly out of sync if you press the button too quickly in an attempt to randomly press buttons to get it. I learned this the hard way.
Take it slow and time your releases. Each level advancement will reset your timer, which is crucial. Advancing to level 2 means you have to hit 5 shots in a row. Focus on your timing, and don't rush it. Focus on advancing your level.
This achievement really isn't too hard, honestly, and I imagine mostly everyone who has ever played MyPark in the past should be able to do this in a few tries. It takes a few rounds to get the hang of the timing, though.