Portal/Escape 01

With nothing of interest in the side room, you must advance forward. As you are about to cross the pistons, if you turn around, you’ll see that a few pistons have silently come down, blocking you from returning that direction. Ominous... You must continue on, only to have the floor opened beneath you.

Turret ambush


The pistons separate, causing you to fall down into an area with limited cover. The door on the right will open first, revealing a turret, followed by the middle door, and the left door, both with turrets as well.

You will have to take out each turret quickly — knock it over or throw it through a portal. It may help to portal yourself beside or behind each turret.

The third door will have an exit. Shoot through the opening and proceed to the next room containing a glass pipe. There are a few turrets, but they seem to be malfunctioning, as they may mysteriously talk, but will not shoot. Shoot a portal above the pipe to walk on it, and jump from the pipe to the catwalk.

Fling


Shortly after jumping down with the following live turret, a door should open in front where there is a broken catwalk. Walk forward to the "over here" text, turn around and shoot a portal on the opened door. Enter a ground portal, and fling yourself to the catwalk.

Rocket turret
You are back in the observation area, with an emancipation field to your left. Walk through it and press the button — this deploys a rocket turret which will seek you and fire a rocket, shattering the glass window.

Walk behind the turret to the next glass window. The turret will fire a rocket, but quickly dodge after it makes the locked on sound, and it will hit the window. Go through the corridor to reach yet another glass window; here you will need to place a portal on the opposite wall, and a portal within the turret's room. Trick the turret into firing a rocket at the wall.

In the next room, you should see a glass tube for moving storage crates. Redirect a final rocket to this tube and grab a storage cube that falls out. Place the cube in front of the vent and climb into it. Alternatively, a chair from the previous room works.

At the end of the vent is a fan; while you can't climb down, you can shoot a portal, and then backtrack to go in another you can reach, to bring you into a small sewage area. Shoot a portal on the wall above the metal platform and walk across it.

Note: Although you can redirect a rocket to itself, it is immune to its own attacks.

No Cheating SpeedRun in One Segment for Mere Mortals
There's not a lot that you can do in this part of the game other than to execute the normal walkthrough promptly and perfectly.

Turret ambush : Disposing of the turrets as their doors open is easy; have a portal on the wall near the door that opens first and put the other portal under each turret as soon as you can. Be standing to the left of the last door as it opens so that you can move quickly in and sight up through the hole in the ceiling for the next portal. First, move the portal from the floor to the side wall so that you don't prematurely fall through it.

Fling : When you crawl into the small passage and look down to see the live turret, the quickest way to get rid of it is again to put a portal under its feet so it falls out of the other portal (as long as you left it on a wall). Move the portal to the wall of the tiny room before dropping down. Crouch as the door tilts up. As soon as you can see a decent distance along the floor of the next room, place a portal out there. Place the other portal under your feet and you will come up facing back towards the tiny room that you just left. Hold the move-backwards key as you do this to land clear of the portal (or see below). Move the portal that is in the tiny room to the sloping door and jump into the portal you just popped up out of. (If you can get the portal on the door while you are in mid-air, there is no need to move back onto the solid floor and then jump forward again and you can shave a second or so off your time.) You will emerge from the portal in the door, but nowhere near fast enough to make it onto the catwalk. Turn the maneuver into a double-fling by moving the portal that is on the floor to be underneath you and the second time you go around you will make it.

Rocket turret : As soon as you leave the steel catwalk, look for portalable walls and use them to move forward to the Emancipation Grid instead of walking. Follow the above Walkthrough, executing promptly and perfectly. When the rocket turret is seeking you, move so as to make it find you as soon as possible and duck away when it has locked onto you and is about to fire the rocket. When using a rocket to break the tube and get a cube, you will need to entice the turret to fire the rocket with the portal at ground level and then move the portal so that the rocket hits the tube. Putting it on the wall behind the tube is good. If you put it on the floor under the tube, move it as soon as the rocket comes through or the cube may fall through, causing you to waste valuable seconds retrieving it. Of course, you want the rocket to hit its target on the first try. Once you are below the fan, portal yourself as quickly as possible into the area of the end-of-level trigger.