This achievement can be incredibly tedious, but each individual mission doesn't actually require a lot of work.
As you run around Mordor, killing Uruks and riding Caragors you'll see little white fists on the map, go to these locations and kill the Uruks guarding or beating a slave, the freed slave will then issue you mission by saying "We tried to poison the grog but they knew it was us, please help the others" or something to that effect.
You will then find the mission on the map which is shown as a white fist in a black coat of arms, similar to the legend mission logos.
The mission is to free sets of slaves tied to poles any way you wish, so you can stealth it and kill everyone before freeing them, kill no one, or run in and cut them all down.
There are 24 missions in total, 12 in each area of Mordor, the first 7-9 of each area should only ask you to free 3 slaves, then 5, and the final mission in Udûn will ask for you to free 7, but in Núrn you will approach a fighting pit with around 11 slaves.
After freeing 2 slaves during the final area missions, other freed slaves will appear and help you fight Uruks or free captives, speeding up the process.
After completing your final mission the achievement will pop as you are paid for completing the mission.
Edit - Thanks to Obi Jase - If the fist icon isn't appearing then travelling back to the first area (or second depending where you currently are) this should then spawn the missing icons, allowing for completion.