This achievement requires you OR your teammates to save 10,000 survivors in missions in which you successfully complete. You do NOT need to be the person that talks to the survivor to count.
The number of survivors your team has rescued in a mission is shown under your teammates names to the right of your materials - it is the green human with a number underneath him. You can typically only get 3-6 survivors per mission except in the mission type rescue the survivors where you can get up to 15 survivors ( you need 6 for the mission to successfully count). In the mission type, evacuate the shelter lately there have been no survivors spawning in those missions for me and originally you would be rewarded with 10 survivors for successfully completing the mission; however, lately I have only been receiving 5 survivors for doing so.In order to rescue a survivor there are various situations that you can find survivors in randomly throughout the map.
Here are a list of all of the types of survivors and how to rescue them:
1. Just need to talk - Primarily found in lower pl levels such as the beginning biome of Stonewood. All you have to rescue these are to talk to them by pressing X near them.
2. Stranded on Vehicle - Can be found on two types of vehicles (a car mainly when found in the interior portion of the map and a RV along the edges of a map), when you approach the vehicle husks will start spawning and you must ward them off for roughly 40 seconds before they stop and you can jump up on the vehicle and talk to the survivor.
3. Campers - Found near tents randomly on forest-covered maps and mainly along the edges of suburbs and cities, when you approach them some husks will spawn. Just kill those specific husks and the survivor will stop fleeing and you can talk to the survivor.
4. Med-bots - Found primarily around the edges of the map. This survivor is found on the ground hunched over on all fours. Walk up to the survivor and hit the X button to call for a Med-bot to come and help out the survivor. You will need 2 Blu-glo (floating blue blobs randomly on the map or by completing siphons or the shard mini-missions) in order to fully power up the Med-bot. After placing the Blu-glo the survivor will automatically be saved once fully healed.
5. Ned-kits - Honestly the most annoying survivor mission to me. Ned is the name of a extremely picky survivor who is often denoted by a blue diamond on the map which may lead you to a shelter or barricaded nook in a structure where he will await your arrival. However, upon you getting to him and just having you teleport him out to your homebase where you have endless supplies and resources to help him out, he will request that you scour the map looking for his one specific med-kit that he absolutely must have and cannot leave without it. His med-kit will be noted on the map with a blue magnifying glass and as you get to that location a transparent blue circle with show you the "zone" in which to look for his med-kit. Pay attention to the arrow on the magnifying glass as that will tell you the elevation level you need to be on (if there is an arrow above it then go higher and if below then go lower). Once any member of your team collects the med-kit then anyone can just go back to Ned and he will happily go with you now. Shut up Ned, no one likes you!
6. Scavengers - If you're lucky then that blue diamond which can take you to shelters or barricaded areas may take you to a location that is unoccupied. Upon arriving here a pop up will tell you that there is no one here and that they must have gone somewhere else. A blue circle will now pop up on the map and the scavenger will be found in the zone. Once you reach the area there will not be a transparent blue circle like with the Ned-kits; however, the same arrow trick applies. Check near natural elevation changes (natural ramps) for these survivors. Once you approach the survivor it will either allow you to talk the survivor straight away or some husks will spawn like with the camper survivors.
***Since version 9.10 there have been times where I've gone to a one of these areas and on the HUD it will say Talk to the survivor but no blue circle pops up on the map. This typically happens on missions where there are 6 spawned survivors instead of 5. The survivor does still spawn in somewhere on the map; however, it does not show you were and the survivor is susceptible to damage. Good luck finding this one if it happens to me I usually just skip it, hopefully there will be a bug fix for this in the future.***
7. Relay Towers- The final type of survivor and probably the busiest requirements to save someone. Primarily found around the edges of the map and can be denoted with a blue diamond on the map but you will probably notice it first by walking around and seeing a transparent, white square floating in the sky. If you approach the area under the white square you will see a antenna that you must first pick up. Now you will be prompted to build a relay up to the white square to do so just walk a couple of tiles away and start building up to that square using stairs and what not until you get there BUT don't walk too far away from where you got the antenna as doing so will cause you to have to go pick the antenna back up. Once you have built up to the square you will then need to place the antenna by hitting X. This will cause it to activate to spawn a survivor directly beneath the relay antenna where you have to do is drop down and talk to the survivor, which if there is any husks nearby he will just starting randomly running around.
All of these survivors except the Med-kit and Ned-kit are mortal meaning that they are susceptible to the husks and mist monsters. I have lost a couple of the camping survivors because they will quit running because I killed the specific husks needed to talk to them, but other husks that were already there killed them first. If these survivors run out of health then they will faint and can no longer be saved.
** This game is technically in still early access so if they do add any new types of survivors or change their requirements then I will update them in the guide above**
This achievement is a LONG grind. At the time of me writing this I have played for 286 days and roughly 2-3 hours a day. I have 919 successfully completed missions (zones explored so not counting Storm Shield defenses where you cannot get survivors) and have only saved 4,202 survivors (this is on average of 4.57 survivors per successful mission) so you're looking at roughly 2,188 missions at that rate. However, once you have completed the main story line and received the achievements for all your storm shields you can then work on your zones completed, survivors, and 500,000 structures built in rescue the survivor missions.
Taking my same stats, I need 5,798 survivors left and if I were to save all 15 survivors in those missions then I would need to complete only another 387 missions, which is still a lot since each mission is 20 minutes long (timer based and currently does not immediately end once the last survivor is saved).
So TL;DR version, don't worry about this achievement as you will eventually get it if you just keep playing missions, but at the same time try to save every single survivor that you run across. You will definitely be cleaning this achievement up later along with the mist monster kills, structures built, zones explored, and missions played with others.
**As of now there have been no events in which EPIC has made it faster to get survivors nor can you get more than just the 15 that you can get from clearing out the entire rescue the survivors mission, but if there is then I will update the solution at the top**