This achievement requires that you shoot a zombie twice with a pack-a-punched VR11 weapon. The weapon can only be obtained from the random box and in my experience rarely spawns. The following solution is a long term solution and not a check & restart solution. Here goes:
Round 1 & 2 - Knife only.
Round 3 - Shoot Zombies 7 or 8 times in chest and knife. Near the end of the round, clear the debris leading to the ship and pick up the gun near the power sign.
Round 4 & 5 - Run circles starting from the Quick Revive island all the way around the bridge and back. Shoot zombies in a line to maximize points. Near the end of round 5 you should have about 7500pts to proceed. x2 points helps here.
Create a crawler and head back up to the ship. Clear the debris on the stairs to the power room for 1250, head towards the power room and open the door for 750, then turn on the power. Turning on the power will activate the pack-a-punch machine and it will always be at the end of the beam of light from the lighthouse. The location will change every few minutes.
Head back down the stairs that you cleared for 1250 and turn left. Walk out the side of the ship and clear the debris blocking the second half of the ship. Jump onto the broken part of the ship and purchase the mp40 for 1000. If you have 4250 left at this point you can get Juggernog, because you need 750 points to get to the lighthouse, jug is 2500 and the door to jug is 1000. Jug is not 100% necessary in rounds 6 & 7 to run circles, but WILL BE NECESSARY in later rounds. I will assume that you got Juggernog.
From where you jumped down onto the second half of the ship, turn left and drop off the edge. Use 750 points to clear the path to the lighthouse. Here is where you will be running circles. (Check a video to see how to run circles here). Basically, you create a train of zombies and when you have them lined up you turn and fire into the group picking up loads of points because of multiple hits.
I opened up the door to the bottom floor of the lighthouse because I found it was easier to create a crawler at the end of each round in here when there was 5 or 6 zombies left. Of course if you get the ray gun from the box you can create crawlers easy by shooting the ground at a zombies feet and the splash damage will take out their legs.
After you create a crawler at the end of each round, hit the box until you get the VR11. Once you have it, save 5000 and pack-a-punch it. use the pack a punched VR11 to shoot a zombie twice and the achievement is yours.
NOTES:
- When hitting the box, always have 500 pts left to buy ammo for the mp40, unless you lucked into a max ammo.
- DO NOT get the death machine power-up as your run really slow with it and it can cause more grief than benefits.
- When you create your crawlers, bring them and George close together and then shoot George. He will swing his camera and turn them into shock zombies that won't die in water. Then run George to the water.
- Best arsenal I found for up to round 18 is mp40 and ray gun. Hopefully you won't have to go that far.
- DO NOT shoot the zombie with the VR11 while it is in the water.
EDIT - To date I've hit the box about 150 times using this method, and no VR11. The solution is valid, it's just down to dumb luck at this point.
EDIT 2 - After getting to round 16 a few times in a row with no VR11, I got it on round 7 in the next game. Woo hoo!