*This may seem lengthy for this somewhat-simple achievement, but I believe this is a good strategy to use at any time, especially if you're just going for number of rounds*
First, the Pack a Punch machine will only work after you've turned the power on and linked all three teleporters together. This can be done with 2 people (I did it with my friend, Benito Arf).
If you want this achievement, set early on that this is what you're focusing on. Don't worry about how many rounds you can get to, or too much about the Random Box (although you should try a few times to get a good weapon). Obviously you just need to use the machine once for these particular 25 points.
The strategy we used was to link the teleporters in alphabetical order to what they are on the map. We made our way to the power switch/Random Box during round 4. Then, when we started to link, we waited until NEAR the end of a round, keeping at least TWO slow zombies alives; two because many times the very last one alive will start to run regardless of its original speed. Just make sure you have plenty of points; the doors right outside of the teleporter are 1250, any others are 750, debris is 1000.
BIG KEY HERE: THE PERSON WHO STARTS THE LINK OF THE TELEPORTER DOES NOT HAVE TO BE THE ONE WHO RUNS BACK TO THE MAINFRAME! Simply split up or have one person return to the mainframe to push X once the countdown begins. Since you should have slow zombies, it shouldn't be frantic. After linking Teleporter A, return to the area in front of Teleporter C (where the Random Box is), and repeat in similiar fashion for Teleporter B, moving when you feel comfortable and are "financially" ready.
You want to leave C for last because this is a great safe position as nothing can come from behind. The Devil Dogs might spawn close, but before round 10 they shouldn't be too much of a problem. Once you're ready for C, you can repeat this whole process.
After linking all three teleporters, you now need enough points to upgrade: 5000. Since the door to C is open, you no longer have it to protect you. But a great place we found was atop a catwalk on the wall opposite and above Teleporter C (up where the Random Box could spawn). There's only one window outside on the ledge that you need to watch, and the rest will funnel up the stairs. Hopefully you have a decent weapon. Either at the immediate beginning of a level, immediately after a Devil Dog round, or near the end of a round, the quickest way to the Pack a Punch is simply to teleport, keeping in mind it costs 1500, so either have 6500 points or have someone else pay for it.
We achieved this with two people so it is possible. In theory this could work for upgrading 5 weapons, too. Run like the dickens when you can, and try to keep a few slow zombies alive so you can run amuck!