Start of by selecting the character you want to get kills with and pick 'Forest Level 6'. Then when in the level aim to get the power-up which shoots 3 shots from front and back which will kill most enemies in one or two shots. If possible try to get the 'Green Force' orb which further increases the amount of shots you fire.
If you start off at Level 1 then you will die very quickly but you do start off with a shield that lasts 10 seconds which kills enemies if they touch you so spend this time looking for the required power-ups.
Once you get your character to higher levels they will last longer being able to get more kills in a single run (the horde is set to 350 kills before you finish the level).
If you have a further 2-4 controllers then plug them in and assign a character to them. Due to a glitch any levels or kills gained by Player 1 will also be gained by the idle characters. So this means that if Player 1 where to get 200 kills with 3 idle players on the map it will add 800 kills to the achievement tracker.