This achievement is for killing Laura in Chapter 10. This is best done in new game+ when you are upgraded. Throughout the entire section of the chapter you will be chased by Laura. What you will want to do is take advantage of all the valves you need to shoot as a lot of them will spew fire below. That will take some health of her. There are quite a few of these locations. You can also take advantage of trap bombs by shooting them while she is beside them. Even after that she takes a lot of blows even from upgraded weapons before going down. Your best bet is a fully upgraded Harpoon Bolt. Fully upgraded Magnum or a shock\ice bolt + Rocket launcher combo.
Also be aware that she can only be killed in the final room before the elevator. You will know you are in the final room when the elevator is visible from the path blocked by fire. It is a room you drop down into from a hole in the floor.