Prior to the 1.4 update, this used to be a nightmare scenario. Between how hard Challenging was and the added difficulty of all the directives, I knew a lot of people who just didn't bother.
AFTER the 1.4 update, this is doable. It's quite easy in fact. I just ran it tonight with one boost partner and two randoms.
I can also confirm that you can run this on a lower tier difficulty setting (the World Tier that was added with 1.4) so you get level 31 enemies instead of level 34 enemies. This makes it much easier to do.
Setup
You don't NEED the very best gear anymore, but you DO need to coordinate your team a bit so everyone has essential skills, remember that with 5 Directives on, each person will really only be able to use ONE skill unless they have a full Tactician's Authority set and a lot of Skill Haste. Even then, the 1.4 update changed how cooldowns work so it's a lot harder to spam skills like before.
Essential Skills
The two most essential skills are the Tactical Pulse and Ammo Cache Support Station. Having these two will effectively negate THREE of the Directives. Tactical Pulse will negate Fog of War, and the Ammo Station will negate Sickness and Waste Not, Want Not, as well as boosting your cooldowns to partially negate Mad Skills. Your best bet is to have two Ammo Stations as this will mean having both a wider area of incoming healing and the cooldown bonus will help the rest of your team recharge their abilities faster, which will let them use both of their equipped skills. Your fourth can just bring First Aid, unless they want to try out another skill set.
Other Skills
Ballistic Shield
Thanks to the 1.4 update, several skills are now much more useful than they were before. One of them is using the Ballistic Shield with the Reactive Targeting mod. Previously, the ballistic shield was about as useful against enemies as the revolver is against the Xenomorph in Alien Isolation. Basically, useless except to quickly revive people who are downed out of cover, because no matter how much skill points you had the shield just didn't have enough health to be worth carrying.
NOW after 1.4, it is. My Agent has 5000 Electronics and thanks to the boost from my Tactician's Authority set, 166,782 Skill Power, which means my Ballistic Shield has a max health of 1,225,201 HP. I was tanking sustained machine gun fire from several of the big LMB dudes, at point blank range, and it barely made a scratch in my shield's health. Add to that the Master Mod that makes the shield regenerate health, AND the fact that threat generation now actively COMES FROM using the shield, and you can now effectively play a tank character and draw aggro. Just like in every other MMO. Also worth noting is that your second skill will cooldown normally even while you have the shield equipped so you'll technically be able to use both skills.
Turret
Remember how the Firecrest set was...not the most useful set? Mostly because it's big thing was carrying more Incendiary rounds. Well, the 1.4 changed that, special ammo types will no longer set your enemies on fire or cause them to explode. They instead now add a flat 10% damage bonus to whatever weapon you're using. This would make Firecrest really boring to use, so they changed that. It NOW causes your Turret with the Dragonbreath mod to have considerably longer range, do more damage, allow you to carry more Incendiary Grenades, and boost your damage against burning targets. People have taken to calling this a Charmander Build. As the increased damage from both the turret and the damage buff against burning targets makes it an extremely viable, and FUN build to use.
Smart Cover
I remember how incredibly useful and lifesaving Smart Cover was...now not so much. 1.4 changed how cooldowns work, so now it won't START cooling down until AFTER it expires. I used to be able to keep it up permanently. Not anymore. The damage buff on it is gone and it no longer gives nearly as much damage resistance. Maybe skip it for now.
Seeker Mine
I loved using Seeker Mine with Airburst, with all my Skill Haste I was able to throw one out every 15 seconds or so. It would cooldown before the fire from the previous mine would go out, acting as a hard cap on how frequently I could use it. Now however, this isn't the case. It only STARTS to cooldown AFTER the fire goes out. That, and the fire it leaves behind? It will now actually damage you, so no more using it in close quarters to surprise rushing shotgun enemies. Still, it DOES do more damage now, so, I guess use at your own risk.
The Cluster mod did get a major buff, it now adds bleed damage and does twice as much base damage as before, so maybe switch to that instead. It's not as visually entertaining but it is more useful.
Signature Skills
As far as Signature Skills go, Recovery Link is your best bet as the 1.4 update upgraded Recovery Link so it will revive DEAD players now as well as downed players provided they're within it's upgraded (50 meters instead of 40) range, which is a lifesaver if half of your group messes up and gets downed in a location that the surviving team members can't reach.
The biggest hurdle in the way of this Achievement is still the grind, as you don't unlock the ability to activate all 5 Directives until you rank up in the Underground considerably.
Stay focused, be smart, and you'll do just fine. And special thanks to ClsNotRapier for reminding me about the Ballistic Shield. I wrote this guide before having tested in actual combat.
...And now the TL;DR version for lazy people.
Have two team members bring the Ammo Cache Support Station, one bring a Tactical Pulse, and the fourth can bring whatever else they want, except Smart Cover. Lower your World Tier down from 4 to 2 so it's an easier Operation.