Growlanser: Wayfarer of Time
It might be a tad controversial to include this game in this list, but it must be remembered that the PSP was home to some of the best RPGs of its generation. The Growlanser series which started on the PS2 was almost entirely adapted to the PSP, but Wayfarer of Time made its translation into English at this time.
Growlanser has always departed from the traditional JRPG norms, most notably in its combat system. Featuring a unique tactical system, battles took place in real time with the player issuing orders to each party member and then letting the battle play out, giving new orders once actions had been completed. It was a fast-paced yet deeply strategic system, addicting and challenging.
The most recent title in the series to be localized in English, Wayfarer of Time was admittedly not as good as its predecessors from the PS2 (Generations of War and Trials of Darkness), but it was still a very good JRPG with hours of gameplay, tons of dynamic characters, and multiple endings worth playing for.