This enemy is by far the easiest to obtain a large amount of kills on. 1000 flood isn't that much at all, in fact this will be one of the methods to getting 20,000 kills since every little flood enemy (the ones that pop on you on contact) counts as a kill.
I have almost completed the Halo: CE campaign and I have about 900 flood kills. If you are going to play the entire game or Halo:CE campaign this achievement will come naturally (Unless you sit back and don't kill anything and have your co-op partner kill everything) finishing the Halo: CE campaign alone.
If you want to get this as soon as possible you can play the mission in Halo: CE mission The Library which is entirely Flood as your enemy and most likely the most amount of flood in any mission in the game.
Make sure to keep an Assault rifle on you while fighting the flood, and shoot all the little guys while they are bunched up, you kill count will stack while shooting a group of them.
Another thing to note: if you plan on going for the achievement That just happened, I can assure you will unlock this achievement just attempting this one.
I found a great video telling information about the flood if you are interested, but do know this video contains MAJOR spoilers if you haven't finished the HALO 3 story. You will also get a good laugh out of this and do note that the video is not animated like the cover. Video was done by Machinima.