You need to first beat the game on veteran difficulty if you want to unlock master difficulty. Beating the game with a coop partner doesn't count either. You must beat it on your own in order to unlock it. If you are just after the trophies, it is actually possible to do this with a friend and still get the trophy. I didn't beat the game on veteran, but I joined a friends game and was able to unlock all of the trophies needed for the platinum.
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