This is a pretty easy achievement. For starters, play only by yourself. Play on the Normal difficulty, and put these skulls on: Mythic, Thunderstorm, Catch, Fog. These practically make sure that even if you don't reach 15,000 in-game, the multipliers ensure you get it. Make sure campaign scoring is on.
Now, once you're playing. You want to play in a certain way. If you're driving a warthog, make sure a marine is in your turret. The points for any kill your Marine gets goes to you. Also, try to make specialty kills. These are needler kills, sticks, headshots, anything that's above your average kill. These give you extra points. Go for vehicle kills. They give you a lot of points. Try not to die a lot.
Follow these points and you'll get the achievement guaranteed.