Have two players or two controllers ready and input the the Konami Code (popular from '90s NES games) during game play to kill your character until you turn into a ghost and then disappear.
Now, with the other character, continue through the level. This character can take damage without any penalties to the other player. Fight through the level until you get to the boss and the achievement will unlock.
It's probably best to do this on the first level because towards the end of the level you'll enter into a subspace highway that will re-spawn your character (no enemies to worry about here) which leads right to the boss(Matthew Patel).
(Konami Code: Hold both Triggers and Enter: up, up, down, down, left, right, left right, B, A.)
(Note: Even though one player is dead the level still loads up twice the amount of enemies, so be careful.)