My method of stealthing the Nest.
Beware: potential spoilers. If you do not want to know how the Nest works and want to preserve the terror and mystery, I suggest you do not watch this video or read any further in this description.
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Ok. So here goes:
This method prevents the Alien from knowing you are ever there.
There are three scripted Alien appearances. In each appearance, the Alien goes for a little stroll and then upvents. To deal with this, we just leave it alone, stay out of it's sight and let it do what it wants. Easy enough.
But there is a second, dynamic Alien that becomes active after you set the Alpha Core to overload. But it remains in the vents ("backstage" to use the game's internal terminology) until it hears a noise from the player ; running, bashing, firing a weapon or using a device. On hearing a noise the Alien will drop and hunt for you. And it will continue to drop and hunt for you for the rest of your time in the Nest. So the aim is to not let the dynamic Alien drop in the first place.
However, this is where the Facehuggers come in. There are several scripted Facehugger events that are intended to force you to use your weapons and in so doing cause the dynamic Alien to drop. This video demonstrates how to deal with these Facehuggers without making a noise.
In fact, there is only one Facehugger you end up having to flame, and that is on your way out anyway, limiting your exposure to the dynamic Alien to almost nothing.
This almost entirely eliminates the level of risk in the Nest. You can quite happily wander round and loot everything you can up until you activate the Beta Core. After I plant the Molotov, I craft a new one and then go looting to replace the items used.
If you choose to explore though, do NOT go near any unopened eggs after the Alpha Core has been activated, because egg = Facehugger = kill = Alien = bad day in the Nest.
Enjoy.