I'm sure there are many good ways to unlock the "Hunting Season" Challenge, but if you have no Save File available (like me) just start a new Lifeline game.
Snap your Achievement App and start a new game. Soon as the game starts shoot as many Zombies as you can (should be about 5% on your App).
After you killed them all, exit your game and press
... NEW GAME.
THANX FOR THE COMMENTS FROM Mr Fiddler & Mysterio400
Rinse & Repeat, hope it helps