Cardboard might not hold up well if nailed to the wall directly. I'd try putting some shelving brackets underneath it and placing the shelf on those.
I think I would try command picture hanging strips.
Yes, command strips, providing your not going to put a lot of weight on the cardboard.
Command strips should work fine, but beware--that thing will not hold any weight. I had a paper sorter made the same way and after not long the little shelves started to collapse even though it was meant to hold paper. I ended up using a heavy duty stapler to reinforce all the "joints" and then it lasted a long while.
Depending on what you are using it for, you may be better off picking up a few metal magazine holders and nailing/screwing them to the wall.
Command Velcro strips !
3M Command strips will work if it's not overloaded. Otherwise use some wood strips on the inside and screwed into the wall.
Don't try to mount it anywhere. It doesn't not have the strength to support anything but the lightest of dust catching nick-knacks.
Thanks! I ended up sitting them in corner & just mount top of shelf to wall.