A few days ago, some footage appeared on the internet of a PSP which had trophies being displayed. This, of course, led to many believing that the PSP would be getting trophies.
However, Sony have confirmed that this isn't the case. "The screen shown on the end of the video showcases the Remote Play function on a PSP," said a Sony PR rep.
So, it looks like there are no plans at present to add trophies to the PSP., shame.