You need to wear every single piece of clothing, save for unlockables, to get this achievement. Just about every store in Fortune City has some clothes you can dress Chuck with. Some are funny, while others border to downright disturbing... in a fun way though.
As all other multi-playthrough achievements, there have been reports of it not unlocking when it should. Try to contain the requirements in one playthrough, to be on the safe side.
This post right here contains a list of all shops and their clothes. I suggest printing it and using it as checklist to save frustration of missed pieces of clothing.
Use the videos below for visual aid.