It wasn't until Chapter 7, when I was going to start heading back through the zones to pick up the Score Pieces and EZI items that I noticed I had accidentally SOLD the EZI Pajamas that show up in the Armor tab.
I quickly jumped on a few sites and googled, while I didn't find too much solid information, I find a few comments saying you needed to have them ALL in your inventory.
I'm glad I decided to continue on and pick up the rest of the achievements before going back SIX hours.
I'm happy to report, that after I picked up the last EZI item the achievement popped anyways.
I'm not sure if this means that you just can collect them and then sell them right away, but I do know that I sold my EZI Pajamas, that was the only one NOT in my inventory and the achievement still popped.