You will need to get 1,000,000 points to unlock this achievement. Most of your points will come from story missions. In order to get the most points it's reccomended you play on hard as you get 100% more points than you would on easy.
If you fall short of the 1 million mark, replay some missions and try to better your score. A good tip is to shoot any cars you can whilst doing the mission before running to the safezone. This will get your multiplier up. Also, try to get headshots and string kills together whilst completing the mission in a good time.
For tips refer to this thread on the forums.
NOTE: If you are replaying missions, only the difference will be added e.g. your old score was 10,000, your new score is 12,000 you will get 2,000 added to your score.