I have both the achievements for finishing the game on Supersoldier and Veteran, but not the one for any difficulty.
I have searched but not found anyone with the same problem, most people have problems with the Supersoldier achievement not unlocking.

yeah hasn't unlocked for me either. did first playthrough on supersoldier and now done it all again on recruit getting collectables along the way but still didn't pop. tried replaying the prologue over & still nothing. think this problem getting slightly overlooked because of the supersoldier not unlocking for some people.