For this trophy you (obviously) need to have three (3) Pack-a-punched weapons at the same time. This won't be a detailed guide, but it will give you hopefully a better understanding. When you start a zombies game, you can only have two weapons at the same time. To get the ability to have three weapons, you need the new perk 'Mule Kick', which is located outside, next to the teleporter and a possible Mystery Box spawn. It will cost 4000 point. To Pack-a-punch a weapon (which costs 5000 points per weapon) you need to put your weapon in the Pack-a-punch machine. This is located in the middle of Area 51, where you start the game and end up if you take the teleporter again. Watch out in this area, because the amount of zombies in this area is literally infinite. If you kill one, another will take it's place.
You can get this trophy only on the map Moon! I tried and managed to do this on Ascension, but the trophy didn't pop.
Also, if you get downed, your perks (as usual) will be removed, and so your Mule Kick too. There's a rumor that when you regain the Mule Kick perk that your third weapon will reappear, this is not the case! So the best this to do is to Pack-a-punch your third/Mule Kicked gun as the last of the three. This will obliterate the possibility of losing one of the Pack-a-punched guns, and having to Pack-a-punch another one.