I just got this. From the "cloudy area" go up one screen, but do it along the very left side. When you get to the next screen, take the tile from off the left side of the screen and work your way up. It's black but you can walk on it normally. Go up twice more, right once, and down once.
Wow that is a really tough one to figure out that way. I recently figured out you can grab black walkable spaces from outside the screen...would never have done this otherwise.
There is an easier way to get to the colorful version of the black and white teleport to archive part you go through to get this...just can't remember how I did it before. Crazy you can't get to the box from the right side of the screen, which you can access from the other side...
In the black and white area for the archives, take the right side teleporter.
That beachy or cloudy area is what we're talking about.
From the first screen where you teleport in, swap your way up in the leftmost column to go up. That will leave you "stuck" in the border of two blue screens. from the right screen (you will be in the left bottom corner, push right, then quickly tap left. you should be facing the edge. Now you can grab a black tile from off-screen. You can walk on this. Place it upwards, and do the same thing afain with the next tile so you can walk up the side to the next screen up. Then once you get there you should be able to make your way up and around (via the outside of the now colored in black and white entrance area) to the chest. In the room with the chest, you will need to do the same swap trick to get to the chest.
Once you open the chest, save. If you walk out through the path in that room it may reset to the title screen, and you will have to do it again (this happened to me).