This needs to be attempted on Heaven or hell, hell or hell, or the easiest difficulty. Otherwise you're going to have a bad time.
Basically rush down the pipe and kill every enemy that appears. You'll want to pull the flying enemies to you and slaughter everyone else quickly. It will likely be more efficent to beat the game so you'll have access to all the moves in the game, but you can do this when you reach mission 6.
The time is a little tight, so you will have to keep moving as you kill, but you should be able to beat it in a couple attempts.