Basically in order to earn this achievement you need to accumulate a score of 1,000,000 points in one Action Mode match. If you can handle speed levels of 60 and up, and still manage to get as many challenge hands as possible, you'll get this in no time.
In order to get it as soon as possible so you don't have to worry about high-speed levels, get every challenge hand possible, at least until well over the 30th speed level. Then by the time you reach 60 you'll have almost all the points. At this point it's just a matter of staying in the game and making challenge hands whenever possible. With practice, it's not that hard of an achievement.