Disclaimer: This solution is based on the one posted in the forum by Fanta Morgana. I'm posting it here so that others can more easily find it.
After loading the level on Nightmare (or Cataclysm, if you're feeling extra ballsy), everyone goes to the right warehouse, i.e. the one with the barrels. Only one person actually goes in, and they set up four of the five barrels. During this step, everyone else stays at the ramp and covers the one inside with ranged weapons. If you have an elf Waywatcher with a Trueflight Bow, she can really help make this easier on everyone.
Once four barrels are in place and the person inside has the fifth ready (but not in place), everyone else quickly runs to the second warehouse. The door will be closed when they get there, but it will open as soon as the other person completes the first warehouse. When everyone is ready, place the final barrel. This will allow the other three to enter the second warehouse.
If you have potion share, now's the time to down your speed and strength potions. Have everyone go to a different pillar and start hacking away. When all four pillars have been destroyed, have everyone exit the warehouse, ASAP.
1.) On Nightmare, friendly fire is active and not very friendly. You'd be surprised how many people forget this.
2.) Stick together whenever possible, except where noted above. The game has an algorithm that punishes bad teamwork. Specifically, the farther away you are from one another, the more likely the game will spawn special skaven and skaven hordes.
3.) If the person in the first warehouse dies for whatever reason, don't panic. Wait for them to respawn and then send them back in. The timer doesn't start until after the barrels explode and collapse the tunnel.
4.) Consider having completed contracts ready that will boost your attack and/or defense. Don't turn them in until you're ready to start the mission to maximize your time. Even if the boost runs out mid-game, the effects will last until the end of that game.
As of the time of this writing, I have not unlocked the achievement, but I wanted to post this solution in case anyone needed some help. Once again, credit goes to Fanta Morgana for providing the solution. All I did was transcribe it and add notes here and there.