A fairly easy way to get this is to not worry about doing it during your campaign and instead go to the "Single Mission" option from the Start Menu and select the first mission ("The Beginning") and play it on "Braindead" difficulty.
Since it's the tutorial level of the game, you are basically guided through the level by on-screen prompts, you only have a couple of weapons to concern yourself with, and there are only a couple of "mob rushes" of zombies you have to worry about. To ensure your survival of the mission, just be sure to keep these tips in mind:
1) Take your time going through the level and cautiously enter each new area - sometimes it can be really hard to see some of the zombies in the darkness until they are right on top of you.
2) Shoot any cars with blinking lights to set off their alarms and draw zombies to them (and then watch 'em go BOOM)
3) If you do get overwhelmed and the zombies start piling on you, just forget about your weapons and start melee attacking instead. On Braindead difficulty, it's not too hard to defeat even a pack of zombies with just your fists.
4) Be sure to thoroughly examine each area - there are tons of helpful loot pickups, including health packs - scattered throughout the level.