WARNING: This has been known to glitch for some people where the percentage would freeze despite having played all the missions multiple times. This could have been broken in the previous patch for some. If anyone has any info on this I'll gladly share it here.
Update Aug 2016: Still seems to be glitched for some people. You can try replaying all the stages over and over again or wait till a new patch comes out.
Basically you need to complete the game, get to level 30 and then replay all the missions on a Hard difficulty. Enemies will be stronger but the game should be a breeze at this point with your better gear and unlocked base abilities. You don't need any part of the base maxed but you should be using upgraded abilities.
Challenge difficulty does not count towards completing mission on Hard Difficulty. So even if you got "Hardened Combatant" completed you'll need to replay that stage on Hard difficulty.
You're allowed to have people under 30 in your party but why would you want to? If you're under 30 you will not get credit for the mission and besides the achievement it's really not worth playing for experience or gear.
The more players you have in your party will increase the amount of enemies in some areas and the difficulty of enemies. So normally you might only fight one yellow guy at a certain part but instead it might have one to three more depending on how many players in your party. In some cases it might actually be easier just to go solo, again at this point you should be able to handle an entire mission even by yourself however your play style or skill level may cater to playing with others it's your call.
I've included a list below that you may want to check off your progress. I don't know if any solid way exists in game to track which you have done. You can do them in level progression order, reverse or just do missions at random, it really doesn't matter.
You can join in mid-mission and still get credit, as long as you're there when it says "Mission completed" at the end.
The game has sixteen missions in total and they should take you maybe anywhere from twenty to forty minutes each average, so about five to six hours in total you should get them all done. Upon completing your last mission it should pop.
Madison Field Hospital 4
Lincoln Tunnel Checkpoint 5
Subway Morgue 6
Hudson Refugee Camp 7
Broadway Emporium 8
Napalm Production Site 10
Times Square Power Relay 12
Amherst's Apartment 14
Police Academy 16
WarrenGate Power Plant 18
Lexington Event Center 20
Rooftop Comm Relay 22
Queens Tunnel Camp 24
Grand Central Station 26
Russian Consulate 27
General Assembly 28