Most of the clothing items can be found on a natural playthrough. It may take one male and one female playthrough to get all the clothing though, unless you trade. There is one item of clothing - the Chef's Hat - which is difficult to come by and there is no right or wrong way for this item to appear.
As with the Legendary Weapons achievement, you will need to have all the clothing in your possession at once for this to unlock.
For a complete list of all pieces of Clothing please see the Clothing List or if you can’t find a certain piece of Clothing please use the Achievement Trading Thread to find people that may have it.