This can easily be obtained on survival as Tanks are frequent and every match normally starts with Bile close by. Simply throw your vial of puke at a Tank at any point in the game and this achievement will pop.
Non-survival method:
I suggest starting on the campaign "Dead Center" and selectively killing the hazmat suit zombies. These zombies will drop puke vials often which you should collect and save until you encounter a Tank during the campaign. There is also an achievement tied into collecting puke from the hazmat zombies.
The ROBBED ZOMBIE achievement in Left 4 Dead 2 worth 20 pointsCollect 10 vials of Boomer vomit from infected CEDA agents you have killed.