The richest game I've played on the PSP so far, after Metal Gear Solid Peace Walker, is The 3rd Birthday. This is the third installment of the Parasite Eve series. If you haven't played any of the two previous games, don't worry. The story will be gentle on you. But the monsters won't.
The best feature of the game is your ability to possess other people's bodies. You'll literally spend most of the game switching from person to person as you take down the Twisted.
The second best feature of the game are the clothes of the main character, Japanese-American Aya Brea. The battles are so fast and intense that her clothes turn to shreds. I'm not shitting you.