Kingdom hearts birth by sleep is a action rpg. But if I had to pick a favorite, Ys the Oath in Felghana is one of them. There is also phantasy star portable. (Basically it plays like phantasy star online, but on the psp) I don't know if you can consider Dissidia Final Fantasy a Action RPG. More like a fighting game with RPG features, but if that's not good enough, Crisis core final fantasy vii exist... and so does the HD remake that just came out days ago.
Still more to come, Star ocean, first departure and the sequel Second evolution also exist. And I guess the last choice would be Brandish Dark Revenant, it's a remake of a old game by Falcom. Honestly unless you consider monster hunter action rpg, then that's probably the best bet for the psp.
Yeah, ys the oath in felghana is coming to switch. And, ys x nordics will be out next year for switch, ps4, and ps5. That is one of my favorite action rpg series.