For efficiency, you'll want to do this one with the 15 trillion points achievement.
The key to getting really long chains is to have a lot of quicken so the game goes faster and you get more enemies entering the area. It's no good just going for quicken, though, since your speed boost will eventually get capped until you get more bonus multipliers. The way to get this achievement is just to play the game normally, trying to raise both multiplier and speed. Play conservatively, don't push the number of powerups you grab at a time and keep your time topped off. As your speed multiplier grows you'll see that it's becoming easier and easier to get long chains. By the time you get the 15 trillion achievement you'll be making 2000+ chains routinely.