It is best to play with friends, I did it with only 1 but would recommend doing with more as it is a lot faster.
The whole point is to get like 3-4 bags of poison (from the house on the left of van) near the water source (behind the barn), then hit the chickens with frying pan, dump them in poison and feed to the monster. When one person is "feeding" the monster, other one should be ready with another poisoned chicken. You have to be careful as the monster will try to eat normal chickens, which will result in "healing" the monster a little bit (in which case you would have to give her some more poisoned chicken than normal, which is 8). If the monster doesn't feed on normal chickens, after around 8 chickens the monster "dies" and you can get it to van (using wheelbarrow).
Congrats! You won this mission!