This Achievement can actually be easier than it seems.
Before attempting this, you WILL want a full group of communicative and cooperative players. My group had the Soldier and the Dwarf as tanks, with the Witch Hunter and Waywatcher providing damage.
Before going for the Nightmare levels, you'll want to get through Hard first with your group, both to practice your teamwork and to familiarize yourself with the levels, as well as gearing up before trying Nightmare. Having Exotic weapons with traits you can make use out of is also a must. The easiest (albeit the most grind heavy) way to obtain the weapon you want is just to combine 5 duplicates of it to get the higher tier of it, then repeat until you get the Exotic variety. Unlike the Rares, Exotics will have three weapon traits on them instead of two.
Two big things to remember is that on Nightmare mode, there is friendly fire on for projectiles and explosives, so if you're a ranged type or like to throw bombs a lot then you're going to have a tougher time. There are trinkets you can equip, they're called Gunnery School trinkets which will increase the blast radius of explosives and also removes the friendly fire effect. Until you get to Nightmare these trinkets aren't terribly useful but will be a lifesaver on Nightmare where you can use them without worrying about hurting your teammates with friendly fire. I've not found anything that neutralizes the friendly fire from projectiles however, but thankfully it's only minor damage if you happen to hit one of your teammates, even with a powerful weapon like the Trueflight Longbow.
Another thing to remember is that on Nightmare you will take considerably more damage from enemy attacks than on Hard mode so you will need to focus on avoiding damage and making sure to hide behind the tanks.
Being familiar with the levels, having appropriate gear, and working closely with your team will let you burn through Nightmare mode much faster than you might imagine at first glance.
Now get out there and purge the Skaven from our city! For the Empire!!