Yeah, Sands of Time only required one play through but the other two in the PoP trilogy do not have stackable difficulty trophies. Very frustrating!
And here I was, thinking I'd be getting the platinum for Prince of Persia Warrior Within tonight, only to find out the trophies for completing the game at various difficulties don't stack. Which means I'm looking at two more playthroughs. I don't mind terribly, because it's an excellent, excellent game, but maybe not right this moment.
Personally, I thought Warrior Within was pretty terrible. Worth one playthrough, perhaps, but the quality of the sound in the HD remake was dreadful. Music dropped in and out, (and the music was shocking), the voice acting was shaky and poorly synced, battle SFX were equally bad.
I wouldn't wish 3 playthroughs of that HD remake onto anybody, myself :/