No Hard Feelings
Save a turret from redemption
During Chapter 5, you will be heading to the turret control room. Along the way, you will come to a conveyor belt that has bits and bobs on it. Look for the laser of a turret that is on the belt and pick it up as you move your way along. When you pick it up, it will thank you and you will get the reward. Then you can promptly chuck the turret aside and continue on.
Complete Test Chamber 10 in 70 seconds
This can be done easily enough, but will take some practice to nail down in under 70 seconds. Give it a few tries to get your pattern down and then make your run for it. If you did it with enough time remaining, when you drop the cube to open the exit, the achievement/trophy will pop. If you are using the chapter select to get to the chamber and you miss doing it in under 70 seconds, kill yourself using the laser and try again.
Show that pit who's boss
During Chapter 9, you will be on a platform surrounded by spike plates. Portal to the catwalk above and start running. When you do, Wheatley will ask you to come back. Return to him and he will try to convince you to jump off the edge. Do as he says and take the plunge into nothingness.
Portrait of a Lady
Find a hidden portrait
After you complete the first test chamber in Chapter 7 with the orange propulsion gel, you will come to a locked gate on the left side. Shoot a portal on the wall behind the fence and another to the right of the catwalk you are on and head through to find an office. Inside will be a portrait of Cave Johnson. Take a gander at it and the achievement/trophy will unlock.
Preservation of Mass
Break the rules in Test Chamber 07
In Chapter 2, test chamber 7; the cube you need to use to exit is a weighted companion cube. Once you head through the exit, you are told not to remove anything from the chamber. So what is a good rebel to so? Remove something of course. Place a portal just outside the exit and then take the cube to the bottom and go through a portal to take the cube with you out of the chamber.
Use an Aerial Faith Plate to launch a turret
The third achievement/trophy you can get in Chapter 2, chamber 6 requires you to nab the turret that gets released in the trash pile. The turret acts differently and more random as it goes through the portals so sometimes it will make it out and sometimes it will head right for the water. When you get the turret to land on solid ground, grab it and take it back to the beginning of the chamber. Drop it on the kicker- or the faith plate as they are called- and the reward is yours.
Make a break for it
This will be gained in Chapter 4 while progressing through the storyline.
Stand in a defective turret detector
In Chapter 5, once you reach the turret control room, you will need to remove the turret from the template scanner. Place a portal in the room that Wheatley breaks the glass on and another outside the room to gain access. Enter and then step into the scanner and allow it to scan you. Once it does, you will receive this.
Catch a blue-painted box before it touches the ground
In Chapter 6, you will come to a test chamber that has a glass case in the center of the room with a box inside it. To get this, you need to drop the propulsion gel on the box so it bounces and breaks the glass and then catch the box before it hits the ground. The easiest way I found was to drop the propulsion gel on it a bit at a time and then quickly drop water on it to stop it from bouncing. Keep repeating this until the box breaks the glass to create an opening and then jump and pull the box out.