Plague chickens are in the zombie levels. To complete the game you only need to unlock the zombie levels on operations one and four. I played a few games on each and it seemed that the chickens show up in the same pattern on both. One chicken in wave 1 and two chickens in every wave after. So, I stuck with the zombie level in operation one and would intentionally die in wave 7 or 8 if not earlier since the waves get longer with more non-chicken zombies as you progress. If you kill the chickens in wave 7 then die you'll get 13 chickens per run. With the 20+ you get for the achievement on the operation four level you'll need to grind this for a while but it wasn't too bad. I alternated the zombies with the 2000 kills and 1000 dogtags to finish them all around the same time.
EDIT: As MattiasAnderson suggests, working on this while you're still doing the campaign reduces the grind and has the added bonus of earning money that you can spend on upgrades or save towards the 3M credits achievement.