This can be done in exhibition, career or tournament but not in any party game. It can be done in 301, 501 or 701. When you are left on 150, 3 bullseyes are required to get this achievement. Hitting three bullseyes as a regular score does not count, you have to be on 150 points remaining for this to work. For those unfamiliar with darts, the bullseye is the little red target in the middle of the dartboard.
The easiest way I found to do this is to move your cursor to the top wire of the treble 20 bed, then gently flick your right stick to give it as little power as possible, more than often your dart will land on the bullseye with this method. After the first dart, just flick your right stick twice more without moving your cursor and you should hit the bullseye twice more. Once the third bullseye is hit you will get the achievement.
I stress it won't work every time due to the cursor moving by itself on finishes to simulate pressure, plus darts will sometimes deflect off those already on the board and be deflected off the intended target, but it is by far the easiest method to use.