You can play as Batman alongside other DC heroes in this top-down action RPG. It captures the feel of a comic book adventure but lacks the free-flow combat of the Batman: Arkham Origins Blackgate (PS Vita/3DS):
While you won't find Arkham City on the PSP, there are two major official Batman experiences available for the handheld: batman+arkham+city+psp+iso+link
The scale and graphical fidelity of Arkham City were far beyond what the PSP hardware could handle. The game features a massive open-world environment and complex combat mechanics that required much more RAM and processing power than the PSP's 333MHz processor and 32MB/64MB of RAM could provide. Alternatives for Portable Arkham Gameplay You can play as Batman alongside other DC
Be extremely cautious of websites offering "PSP ISOs" for modern games like Arkham City or Arkham Knight . These are often: : Videos or links used to generate ad revenue. batman+arkham+city+psp+iso+link
If you’re determined to play a Batman game on your PSP legally, here are the real titles (available via UMD, PSN, or legal backups from your own discs):