Once you save all the Little Sisters and spare the lives of Grace, Stanley and Gil the achievement will unlock. If you have decided to harvest any Little Sisters or to kill any of the characters you will need to start over.
Grace Holloway - Stanley Poole - Gil Alexander
You will run into these characters as you make your way through the game. They will hinder you as you try to progress through the levels. Once you have completed whatever tasks you need to, you have the decision to kill them. Make sure you don't kill them either through requests or your own decision.