You can change game options to make this easier. Press

and change Starting Lives to 5 and Difficulty to Easy.
You need to beat a score of about 39,000 for this achievement. Choose Maze 4 as the starting maze. Complete levels by collecting all the fruit, then exiting via the green door.
I noticed I would gain a triple bonus when I completed the level without firing a shot. Obviously, this is much harder to do on the later levels, so try for it on the first few levels.
Pay attention to the message telling you which maze the watermelon appears on. The game does not proceed chronologically, but if the right level comes up, make sure and collect the large watermelon as it is worth 10,000 points!