Update 1: Michel posted to say, this can be done with any character.
Update 2: Light Buster says during Kirito mode this can also be done.
Upon getting your Affinity Level with Kureha (your best friend) to level 4 you can find her in the Squadron PvE area where you can interact with her and offer to give her a outfit.
So make sure you have a spare outfit. After you've selected it she'll put it straight on and your achievement should unlock.
NOTE: My achievement took a few extra seconds to unlock and wasn't instant so just wait to it pops.