You start off inside the Face Hugger shrine. Switch to Navigation Sense and start forward, through the tunnel.
Out of the tunnel climb up the wall and through another tunnel. It will branch into two ways here, both ways go the same place. Pick one and you enter a room with a pillar of fire. Go straight across the room and you'll see two pillars opposite the entrances. Climb one, and the top is hollow. Go through that tunnel. Both lead to the same place.
From there if you look on the ceiling you will see two grates. Both lead to the same room. Break the grate with a claw swipe and go through the tunnel. Climb out of the ditch.

For the walkthrough I am going left from the tunnel's exit.

Turn until you face the two columns in the room. There is an opening behind them, up the wall a bit. Climb up to it and go through the tunnel. On the right you will see more flames. Turn right and follow this tunnel. You will need to crouch while you run to hang on here. You will be in a room with two things hanging down.
Turn along the wall and run to the alcove. Follow this tunnel. Stay on the ceiling here. There you will see two blocks above two more jets of flame. From the ceiling, use your claws to take off the supports for the two blocks, shutting down the flames. You will notice another hole on the ceiling. That's where the other path lead.
Now, turn around and go back to the flame you saw before (remember, in the room with the two things hanging down the exit was on the ceiling). It isn't there now. Drop down and drop down again. You may want to switch to hunting mode now, because here's where the humans are. It doesn't matter which way you go, but crawl down over the edge and look down.
There should be people walking around. Try to find one to drop behind and kill them. You have two exits here, because labs 1 and 2 are locked. While standing on the platform, facing Lab 1, you want to go to the path on your right. Go up either set of stairs and at the top you'll notice another room there. Go into that room and along the wall near the ceiling, are four more grates. There are actually two separate tunnels. Go across the room and take the left tunnel on the far wall. Time to go back to Navigation Sense.
Follow the tunnel left, then break the grate on the ceiling. Go up and left again, break another grate. If you drop down here and go left, you'll be at the far left grate from the room's entrance, so go straight ahead. Now you have some more choices. Go up and break the grate there. Follow it straight, then down and break another grate. Switch to hunting view because humans often are on the ground here. Drop down behind the marine and kill it first. Kill the civilians at your leisure. ;) You are now in the left hand area of the stairs you took to get to the rooms with the grates. This has "Lab 1" marked on it. This is part one of two security systems for lab 1. In order to open lab 1 look around from the ditch until you see a red light on the underside of a control panel. Break the light and the panel, then back into the tunnel in the ceiling. Back to where the unbroken grate is.. break it. Follow the long tunnel all the way to the end, break the grate above and too the left, go through it. Follow that little bit and now you're above the left hand room of the opposite entrance. This has "Lab 2" marked on it. Follow the same pattern you followed last time to take out the panel.
Now, this room has a turret. You may want to climb up from out of the ditch and take the time to disable the turret. Climb back up through the tunnel. Follow it all the way back to the beginning. Climb out and through the other grate on this wall. Follow the tunnel, break the grate above you, climb up and to the right, break another grate. Once again dropping down and to the right brings you back to the grate room. Go straight, then the grate above and to the right. Follow this one and you are above the second "lab 1" area. Break the panel and lab 1 opens, but we aren't going there yet. This is the right room in the area with the grate room. Go back through the tunnel to the unbroken grate. Go through it all the way to the end, and you are above the final room.
Break the panel, and lab 2 is open as well. Also remove the turret threat the same way as before. One powered up tail shot does it. This is the room on the right of the opposite entrance. Now it is time to go to the labs. Let's go to lab one first. Inside are androids, so be careful. Take them out with your claws. Androids do not show up in hunting view, so stick with Navigation Sense. Once they are dead, you'll notice there are a lot of corridors here with Caution signs there. These are here for a good reason. Go through them and breaks the panels. You'll occasionally find a civilian inside. They are unarmed, line up your teeth and eat up.
Once you've cleared all those room, look around the lab. You'll see the computers have pipes coming off of them. Break those. Once all five are broken, repeat the process in Lab 2. Once the last pipe is broken be careful, marines will begin showing up. Make it to the platform in the middle of the first room and ride down. Kill the marines below and turn to the door on the right. Break the control panel and go through the open door. You'll be in a room with corridors and a lift down. Take the lift down (or climb around) and then go on the door to the right. Now here is where things can be difficult to explain. At this point we're going to do some wall walking. Once you get to the next room, climb on the wall on the right all the way to the end, then go down.
On the way down destroy the block holding the door open. Behind these doors is a pair of turrets that will end the mission quickly if you are not cautious. After opening that side of the door, climb up again, above the door, and remove the other blockade. The turrets are now unable to get to you. Take the passage way to the right. Run quickly along the right hand wall. More turrets, another door, more blockades. Removed the blockade, climb over the door, remove the other one. That seals the temple. It is now time to return to the hive I didn't run into any enemies past here. In the middle of the floor is a hole. Go over to it and it opens up. Jump down it. Switch to navigation sense if you wish and follow the tunnel, dropping down another hole in the floor. Climb up the other side, and follow the tunnel. You will come out near a giant alien statue. Climb up the wall on the far side and you will see a balcony of sorts. Follow the tunnel there and you'll end up back home in the hive.