This does not have to be in one game, nor does it have to be all in a row. Simply get a lifetime score of 1,000,000 points to get this achievement.
I'd consider myself fairly mediocre at this game, and I manage around 100,000 per Marathon/Survival game and 50,000 per Timed. Just keep playing and getting better at the game and you should get this eventually.
And remember that combos with Starflowers are worth a lot of points.