This one is actually incredibly simple and the better way to play the game.
So basically in the game there is a currency called Adam that is used to buy and upgrade your plasmids and tonics in the game. This currency is only gained from Little Sisters. With the exception of the first Little Sister you have to fight and kill a big daddy that is guarding the Little Sister. After this you are given the option to harvest or save the Little Sister. For the achievement you want to make sure you save every Little Sister you encounter, you DO NOT have to deal with every Little Sister in the game you just have save the ones you do. I recommend you save right before making the choice just incase you press the wrong button in which case you can reload and try again.
On the topic of Adam you get more upfront for harvesting the Little Sisters but every 3 you save you are given a gift of Adam which comes out to more.
Edit: A couple people are saying this achievement didn't pop for them at the end of the game so make sure you save right before the final fight and if it doesn't pop just run through the final fight again
Edit 2: Some people are saying it's specific to survivor difficulty some are saying it's not. I did have the game on survivor difficulty when I got it so try turning the game to survivor difficulty right before stabbing Atlas for the 4th time
Edit 3: basically the servers are sensitive so it doesn't seem difficulty specific but you may have to retry the final fight if it doesn't pop