Sadly I must say this achievement requires a bit of luck. It took me four attempts to get it as the game can be quite brutal. After all, the Uprising is doomed to fail on October 3rd.
That said, here are some tips to aid your chances.
1. Play on Easy/Easy. Difficulty does not affect the achievement.
2. You will need to play all 5 day missions. This cuts the number of missions to reach the "end" to the bare minimum. You can only accept a shorter mission (3 or 4 day) once. Save that one time near the end and only to help preserve a district so it can limp to the end.
3. The end mission activities can be cheated. If you get one that hurts you, before going to headquarters, dashboard out of the game and restart it. The previous mission will end again and you'll either get another chance to get the reward for the activity or even a chance at a different one. Focus on one's that boost morale in districts (1st priority), up the momentum (2nd priority), or offer a damaged weapon (3rd priority).
4. When you are doing missions, take a little less at the start so you can gather more resources. Also prioritize more valuable items. Remember that heavy ammo is worth more than long ammo and short ammo. Med kits are worth a lot too. Look at the number of loot opportunities on each mission (at the bottom right) and find them all if you have the movement points to spare at the end of a mission. This will help for tip #5.
5. Repair and sell weapons between missions. You want to complete all Excursions available at the mission screen between each mission. This will keep you poor, but the morale is absolutely necessary to pull off this achievement. Skipping one opportunity will in all likelihood kill your chance to do it.
When I finally succeeded I still had five districts remaining. However if I had to do another mission I would've lost two more districts by mission end. Stick to the 5 day duration missions and hope for a little luck. Fortunately a game only takes about 2-3 hours.