Update: I was unfortunately not aware of Shamus Young's severe criticism of Fallout 3 available here to link in the original piece and I regret that. It dovetails rather nicely with what I've written and it's much better executed than my piece. I strongly recommend anyone...
This is one of Dead Space 3's more difficult achievements. The Feeders in Dead Space 3 react to you, but if you don't make any noises and navigate the level correctly, you can avoid them all together.
As you first start Chapter 9, you'll see a feeder scamper off a counter top and around the corner. Follow him through the next room where the bodies are hanging. You won't see him again. As you enter the next room, hug the wall to your right until you hit the far wall, then proceed through the door on your right. There are no feeders in this next room.
Once you enter the next big room with feeders, head through the left opening, but move slowly as another pair of feeders are waiting just out of sight around the corner. If you keep them in your field of view and back away, you'll make less noise and are therefore less likely to cause them to attack. The next door will be on your left (after backing away).
In this next room, proceed straight forward and through the door on your right at the end. Congats! You made it through without alerting the feeders. If you're still having trouble making your way to the pumpstation, watch this youtube guide for a better idea of your ideal path: