From Foxfire49's guide for the Xbox 360 version:
This achievement is called "Long Live the Empress" and you get this for saving Emily and beating the game.
Low Chaos - Really simple, enter the Greenhouse. Either sleep dart or directly confront Havelock either way grab the key and go unlock Emily's door. (Achievement Unlocked)
High Chaos - Climb the Lighthouse, stay hidden and headshot Havelock with a crossbolt. Really handy if you have the Lens Magnification upgrade. Emily will appear to fall...run to the edge and press X where you see her hands.
Or if your not going for the "Mostly Flesh and Steel" Achievement...just use possession on Havelock and walk him to the edge and end possession so he falls to his death then go after Emily.