With the no-fail style of gameplay, this should be pretty simple to pull off. All you need to do is ignore the scratching and tapping and look for the Effects Zones and Freestyle Sample Zones.
Effects Zones occur when you see the orange arc over top of one of the tracks. When this appears, simply twist the effects knob of the DJ Hero Controller. You'll see a point at the top of the arc move in the same direction of your twist, and the multiplier will double (if not already doing so).
Freestyle Sample Zones are the long highlighted sections in the red centre track. When one of these comes along, just tap the red button at least once.
If you hit all of these through the course of a mix on Hard or Expert difficulty, the Achievement will unlock once the mix ends.