At the start of chamber 6-2 place a portal under the cube spawn pipe. Take the cube and drop it down the ledge on your left. Place the cube on the button and go up the new stairs.
Place your second portal on the surface below the vent pipe. Press the cube respawn button next to you, and the cube will be placed on the other side of the fizzler field. Go through and place the cube on the button to exit the chamber.
Once outside the chamber, follow the path until you are on the metal railway above test chamber 6-2. Place a portal below, jump over the railing you just came from, and use your second portal to get back inside the chamber. Follow the same solution; after leaving the chamber, your achievement will pop.
The video guide starts at 1:13