There are 3 Us Prisoner on the map to liberate. The prisoners are always in the same spot and camp. Before you leave the area / mission via the Helicopter at the end make sure you have liberate all three prisoners otherwise you have to start a new game / run. Technically the achievement is missable.
I create a map with all three locations (Attention, the map is big)
Joker and Moses should not be a problem, free the camp where are both prisoners located and then liberate the prisoners.
Yokel is a little bit tricky because when you enter the camp, the NVA Commander will be execute Yokel really soon. So enter the camp and kill the NVA Commander asap! If Yokel dies, reload immediately the last checkpoint and try again.
00:08 - Joker
00:36 - Moses
01:05 - Yokel
If you want solve the other challenges too, here are the locations from the speakers, lighters, South Vietnamese POWs and AA Guns (Video links to Youtube)