I did this. I took one of the shelves and made it into a back for the bottom shelf. Two crosspieces at the bottom and one at the top, and it feels stable.
I think the main things I did to make it work this time were:
* loosen the crosspiece at the bottom that I think made it lean to begin with
* made damned sure all crosspieces had right angles at the end,
* ...and were exactly the right size, so they could just fit in their respective holes
* clamped a spirit level to the side and made sure the case stayed level as I put all those crosspieces in.
Since you only braced the bottom, I suggest you put some weight on the upper half and see if you are still satisfied with its stability before you make the other three shelves.
I also put a crosspiece at the top, but it's still a good suggestion. I'll wiggle it when I get home. Thanks!
the suggestions below are all workable.
Using a sheet of plexiglas for a back would allow let you see the wall behind the shelves.
Next time around, Woodshop I: Shelves inset into dadoes on the sides.
Dadoes are simple to cut if you've access to a radial arm saw., Just make sure the boards are a tight fit. You won't need any nails or screws, just wood glue to secure the shelves