The most accessible version is the Deluxe Edition on Steam
Since a PSP version doesn't exist, you won't find a legitimate .iso or .cso file for PPSSPP. Instead, you can play the game on these platforms:
You can find the Deluxe Edition digitally for , , and . Playing on Android or Mobile
While you cannot play it on the PPSSPP emulator, you can still experience this 2.5D Metroidvania on modern devices through other means. Where to Play Arkham Origins Blackgate