Crackdown 3: Campaign

Survive the city lockdown Niemand starts once you eliminate the last of the 5 underbosses (as in, Berg, Roxy, Keita, Khan and Sorensen) I had bad luck with Roxy as my last underboss as her tower was a bit difficult to defend. I'd consider either a different boss as your final one or immediately leave for the ground once you terminate the final underboss. Make sure you are somewhere you can defend with easy reloads as its a pretty heated battle. There are reports that the 'final' lockdown can be triggered by one of Niemand's direct underlings as well - so YMMV with which lockdown pops the achievement.

If you didn't survive the 'story mode' lockdown, you can trigger the final (achievement related) lockdown by picking a battle with one of the faction groups and pulling that battle to another group of faction enemies (not the easiest to do in practice as this means you need 2 different kinds of enemies on you and they don't typically spawn near each other. Additionally, you can trigger this lockdown again by listening for word of a supply convoy in your area. Be armed appropriately and take it on! Do not relent. Keep destroying unit after unit the city is put in lockdown. Survive this lockdown and you'll unlock the achievement. I was near the Chem plant but you can presumably find convoys anywhere on the map. It does not matter if you've removed Niemand or not. The achievement related lockdown will happen regardless.

Spazpol suggested stealing a tank as the added firepower makes easy work of the forces sent at you.

keung noted that if you are playing in co-op and your partner dies, this will void the attempt. Neither you nor your partner can die.

The simplest way to achieve this is of course to break the last lockdown during the story mode (which seems to trigger after most/all of the bosses have been defeated.

If you've already defeated Niemand, the achievement is still obtainable and you don't have to make a new game world. The tricky part is actually triggering a lockdown after the map has been reclaimed. This requires a level 3 alert from 2 enemy factions at the same time, and is almost impossible to do accidentally after the game is beaten. After a lot of struggling to trigger a lockdown, I found a method that seems to work more reliably. It is easiest to do this once you have access to the agency vehicle's Minotaur form at level 4 driving skill, but it is possible without.

1) Trigger an alert with any faction. Attacking and destroying a convoy is a guaranteed method. You can also kill larger groups of enemies (e.g. on the floors of the security HQ) to start an alert.
2) Once the alert is activated, make your way onto a nearby road highway and summon the agency vehicle. The minotaur/tank form will give you the durability to survive without running away so fast that the enemies lose you.
3) Drive on the highway to Ashwood Marina on the eastern edge of the map - the partially blockaded section of highway here reliably spawns enemies from the security and industry factions. Use the tank to blow them up while driving through, and it should be enough to trigger the second faction alert, and the lockdown.
4) Take down the invading enemies to break the lockdown. Note that only reinforcements called on you as part of the lockdown count towards the completion percentage: You won't get any credit for killing other enemies.

Feel free to reduce your difficulty setting to Rookie, it makes surviving easier and does not prevent the achievement.

It seems, that lockdowns are engaged, when you kill a lot of enemies from different armies in the game. For me it happened after killing bosses or when i just cleared one of the outpusts.

Final lockdowns are all lockdowns, which happen after the cutscene, where Niemand offers citizen's safety in exchange for agent's life and body.

For me it happened after Roxy boss. I failed it. But it's fine to fail it, it can be triggered again and again.

I triggered it again by blowing up armored convoy (logistics division in my case), that made my wanted level at 3 with that division, then engaging enemies from other division. When their wanted level raised to 2, lockdown started. I moved to one of the monorail stations (Health Field saved me on a way there) and defeneded it with the help of the militia. It also has ammo refill, so it's very useful. It seems that militia kills do not count to closing the lockdown, so you need to kill some things yourself. When i reached 100% achievement popped.

I haven't killed Niemand or any of the captains.

I tried icey's mehod but didn't work for me. So, if you have missed this achievement, the only way that worked for me was starting a new game on Rookie with my previous character and killing every boss except Elizabeth Niemand and Liv Sorensen. First I killed Wilhelm Berg (story related), Alois Quist, Kuli Ngata and Katala Vargas because I thought that it was going to be enough, but it wasn't. Then I killed Reza Khan, Djimon Keita and finally Roxy. After killing Roxy the final Lockdown appeared with a new kind of robot.
If you die during the final Lockdown you'll miss the achievement.

I think it doesn't mind the order of killing the bosses or which bosses you kill (EXCEPT Niemand). The last Lockdown is when after killing a boss the game shows up a cutscene with Elizabeth Neimand asking you to give your life to save everyone or she'll kill everybody.

Also, if you want to kill Alois Quist, Kuli Ngata or Katala Vargas, it's not neccesary to do any mission, you can go directly to their towers and kill them.