This achievement requires you to pack (and/or re-pack) a weapon at the five different pack-a-punch locations on the map (4 regular Pack-a-Punch locations, and the Golden Pack-a-Punch location).
To unlock the four regular Pack-a-Punch locations, turn on the power switch at spawn (Docks), and the power switch on the top of the boat (Bridge). You also must go to the Lighthouse Approach aka the blue rock cave, and pick up the blue rock (knife it and then pick it up once it falls), and give it to the hermit, at Lighthouse Level 4. The four main Pack-a-Punch locations will now be activated, one at a time. The Pack-a-Punch location will rotate about every three minutes or so. You can tell which location Pack-a-Punch will be at by a blue light shining on it from the lighthouse. These four locations are: behind the Boathouse (right pathway from spawn), the Beach, the Sunken Path/right outside of Artifact Storage (underneath and behind the back of the boat), and the Lagoon (left pathway from spawn).
Now to unlock the Golden Pack-a-Punch location, you must first get two wheel cranks for the Zipline. The first wheel crank can be found on the Stern (front of the boat), and the second wheel crank can be found on the Forecastle (back of the boat). You must now place the wheels on the crank pillars, then rotate the Zipline wheels into position. The two crank pillars can be found on the Sundeck (top of the boat), and the Main Deck (middle of the boat).
Once both wheel cracks are rotated into position, you can go back to the Hermit, and he will give you a Zipline handle. With this handle, you can go outside of Lighthouse Level 4, and zipline up to the Facility Entrance. Once there, make your way into the facility to the Human Infusion area to activate the third power switch. This will unlock the Golden Pack-a-Punch area. The blue light will now rotate onto the Golden Pack-a-Punch just like the regular Pack-a-Punch locations.
In order to get to the Golden Pack-a-Punch location, you must wait until the blue light from the lighthouse shines on this area (Iceberg), which will be on an ice island slightly outside of the main map, as seen from the boat. Go to the Sundeck on the boat, and there will be a flinger you can stand on . After a few seconds it will launch you to the Golden Pack-a-Punch (Iceberg), where for 5000 points, you can fully pack/upgrade your weapon (normally would cost 15,000). A lot of zombies will spawn on the island, and you won’t be able to get back for a few minutes, so be prepared to fight. You will automatically be launched back to the main island after a few minutes. For solo, only you have to stand on the flinger, but if you have more people in your party, everyone must stand on the flinger at the same time to be launched to Golden Pack-a-Punch (Iceberg).
To Pack-A-Punch a regular weapon is 5000 points, and to repack it is 2500 points (you can do this up to 4 times to increase its damage, and give you an alternate ammo type). After your fourth repack, it will only cost you 1500 to repack, which will give you a different alternate ammo type, but won’t increase the weapon damage.
You can pack/re-pack in any order, at any location. Once you’ve packed/re-packed a weapon at all five locations, the achievement will pop. If you are looking to do this for as little points as possible, I’d recommend going to the Golden Pack-a-Punch location first. This way you can spend the 5000 points to fully pack-a-punch your weapon, and when you hit up the other locations, and pack the same weapon, it will only run you 1500 points more on each pack; that brings your total points spent up to 11,000 points to get the achievement.
Not my video, but the shortest, and to the point video I could find: