This method in the video above was the go-to for getting Adversary Mode outfits on Xbox for quite some time. I'm not entirely sure if it's been patched or not because I haven't tried it since posting the video two years ago but you're welcome to give it a shot.
If it doesn't work then I don't know what to tell ya, unfortunately. There may be another method out there but I haven't been following outfit glitches for a while so I'm not up to date on working methods. Anyone else is welcome to share if they know something that I'm missing.