The PSP has no Trophy system. Trophies debuted with PlayStation 3 firmware 2.40 (July 2008). The PSP's architecture and PlayStation Network implementation predate this.
If you want trophies for PSP-era games, play their remasters/ports on Vita, PS4, or PS5 (e.g., God of War Origins Collection, MGS HD Collection, Persona 3 Portable on modern platforms).