Dragon Ball Z: Shin Budokai – Another Road runs on all PSP models:
No specific firmware version or hardware revision is required. It's a standard UMD release (UMD Video/Game hybrid format). If your PSP plays other UMD games, it plays this one.
Note: The game is Japan-only (UMD region 2). On a non-Japanese PSP, you'll need CFW (Custom Firmware) to bypass region lock, or a Japanese PSP.