You do this by shooting explosive barrels and killing enemies, right. I must have nailed 12-24 with this method yesterday with no progress in the quest. Have I done something incorrectly?
I started up the very first level and got to the point where you find the blue keycard. Through the blue door you will drop down and find a bunch of regular zombies. I would gather them up and go down the hill to another group of zombies. Round 'em up near the red barrels against the corner and you can get 8-12 every time. Just reload checkpoint after you see all the bodies on the ground and it'll start you right at the blue door. Rinse and repeat until you get 50. Less than 5 minutes.
Snapmap method worked perfectly