To help you with this struggle, a few pointers I would suggest:
* Only those you rescue from cages or from behind depot doors count for this trophy. Despite having multiple objectives that say to Rescue targets, the cages are all that matter. I cannot establish if this is including those in the Inhuman Condition.
* Make sure you are near the cages when they are broken, so you can have it count for you. There were some mentions of the cages not counting for some in other mediums.
* The most I have found has been around 3 to 5 per mission, specifically The Inhuman Condition and Day of the Remains.
* Leave this trophy for the end. Make a challenge for yourself to do Day of the Remains five times a day or more, perhaps; this will ensure 15 rescues, meaning seven days would be your maximum requirement if you avoided rescuing them to this point.
EDIT: Outdated suggestion given the changes to the War Table on "Day of the Remains". I will attempt to adjust the guide accordingly.
Old solution:
*** Spoiler - click to reveal ***Now, for the suggestion on how to run the suggested mission, Day of the Remains. First, head to the first and second objectives. At the first objective marker, if you continue left instead of right to the objective, you can find a SHIELD bunker with a cache Strongbow. At the second objective markerz two cages will be found over another SHIELD bunker. After breaking the cages and clearing the enemies, you can follow the objective marker again. Once you have a choice between going left and right, go left and head to the nearest building, where a destroyed depot building will have a prisoner hiding within it. By letting Theo take the prisoner away and waiting a few seconds, you can then return to the Quinjet and repeat it.
A suggested mission to do this on, if you've already cleared the "Day of the Remains" mission, would be the "And We're Back" mission. The reason for this lies in its repeatable state, and you might still be farming other miscellaneous trophies in the mean time while doing so.
Upon starting the mission, you'll be rescuing inhumans under attack. Once you've dealt with this, make sure you ping the area so you can see what other side objectives exist before continuing on with the main quest line in this map. While you won't know until you get close enough to them, what you're wanting to find are containers that you need to blow the power cells up to free the targets. You might only find one waiting for you throughout the side objectives, but fear not: by continuing the quest line to the end of the mission, you'll have to free three more prisoners at the very end. The reason this is suggested because there is a chance of this quest re-appearing during a War Table refresh.
This is a grueling grind of a trophy, so this should be looked for throughout playing the main missions and will be one of the last ones you'll need near the end, probably. If there's anything else I can try to fill you in on, let me know. Happy hunting!