This mostly involves spamming projectiles in combination with dust storm. They track enemies and hit many times to increase your combo quickly. Un-equip all your gear to do less damage and avoid killing monsters before hitting 1000. Getting hit and having your chain broken, even after surpassing 1000 hits, will NOT earn you the achievement.
This can be done very easily, very early in the game with these two giants.
If you're already past that part, you can also get it fairly easily on those monsters with funny mouths in chapter 2. You'll regularly run into big groups of them. My combo of choice is X, Y, B, down+Y.
Further still, in chapter 3 you'll constantly run into big groups of zombies which should also make a thousand hits easy. This video is at the very beginning of the chapter.