You must place a flower in a way that clears all remaining flowers from the screen, either as one set of three or more, or in a cascade. You must do this in both a Standard and an Expert mode game. It does not have to be done at the end of a level.
Try to plan ahead with the multi-colored flowers so that getting one set of three or more leads to a second set. I had to do this to clear the board on the Expert mode.
If you have not accomplished this by the end of level three, go ahead an fill the board with flowers rather than restarting. This will ensure you get credit for finishing games, leading to
Edit: Har Miggido
and Mike Pitch
both commented that they were able to do it as late as level 5, so if your board is not too out of control, it may pay off to keep going.
Edit: If you already have those two don't bother filling the board, just back up and start a new game as OwnMyGamerScore
both confirm that the points still rack up for
Edit: In a helpful hint from the comments AP E JC
said "I noticed that in the moment that the game is starting, while the flowers are growing, you can place flowers in the occupied slots. So if you have a good queue and fast fingers, you can take advantage, and clear some bad pieces."
mentioned something in the comments that I hadn't considered. "I can confirm picking up the last remaining flower with the trowel will pop the achievement."