The wall past the emancipation grid (once you've gone through the door) will accept portals. Put one in there, get the cube and let the door close, and portal through.
Explanation
In the entity list, there is a linked_portal_door for this purpose; it is used in the Death Trap (in map sp_a4_finale2.bsp
):
This entity is designed to link two separate, distant areas together without any clear transition between the two. This entity is exclusive to Portal 2.
It is used in Chapter 9, in the Chamber 75 Death Trap with all the crap turrets. The room is actually completely separate from its supposed surroundings. It is the only use of this entity in the final version of the game, though commentary states that it was used a lot during the development of the title to link chambers together.
I guess that the development team first made the rooms separate so that they could wipe a bad room, then connect them later when the levels were more perfect, and I suppose that this room didn't fit.
Pictures
Here is a picture of the Death Trap that isn't connected to the other rooms:
Near the threshold and a tiny step (noclip fly) to either side:
Video
You might want to skip the commentary and long walk and go to 04:30. From here on he shows the box from outside at the three locations (before box, in box, after box); he first does this slowly, then at a later point he goes between all of them in quicker succession. This might show the trick better than above pictures.
Thanks to Jon Ericson in the comments for finding this video.
Best Answer
It's at the end of the 9th Chamber of Course 4: Excursion Funnels.
Remember the part where you have to create a light bridge that crosses in front of the turrets on the conveyor belt, and they all just hit it one after the other and die? Normally you'd have to move that light bridge slightly to the left so that you can continue with the level.
Instead of moving the light bridge, place the exit portal of your excursion funnel beside it - so that you start moving backwards into the unexplored depths of the level. You'll pass by the cube, which you'll be able to see through the light bridge. Then you will die.
The achievement should pop here automatically. Here's a video of the process.