It is suggested that you use the 'Catacombs' Stage for this achievement. The method is quite easy actually. There are spike traps located around the stage. Have both you and your partner stand in front of the traps and make sure you have a clear line of communications with them.
The player who is not going for the achievement (Player 1) must purposely walk into the trap, which will down them in the process immediately.
The player who is going for the achievement (Player 2) should about 5 seconds and then walk into the spike trap as well.
Player 1 should, at this point, be getting attacked by zombies and losing health as their "Stand-Up" meter reaches 100%. If done properly, Player 1 should die while Player 2 is still in the downed state.