PPSSPP (Stable) cydia tweak is the best, original and only PSP emulator written for iOS in C++.
PPSSPP translates PSP CPU instructions directly into optimized x86, x64 and ARM machine code, using JIT recompilers (dynarecs).
PPSSPP can thus run on quite low-spec hardware, including stronger ARM-based phones and tablets, as long as there’s support for OpenGL ES 2.0.
Not all games run perfectly yet but it runs a lot of games.
No games are included with this download, you will have to dump your own PSP games and turn them into .ISO or .CSO files, or simply play free homebrew games, which are available online.
Please note that ARMv6-based devices may have various kinds of issues, and more modern devices are recommended.