Since you mentioned monster hunter, toukiden and god eater, you practically answered your own question.
If you're looking for more hunting/hack'n slash games on psp then there's also phantasy star portable, lord of arcana, dynasty warriors strikeforce and the Ys series but they're more on dungeon crawling than hunting.
Frontier Gate Boost+ (Final Fantasy + Monster Hunter)
Sadly, not yet. [USER]Cursed Kaiser[/USER] created a great blog about it, though.Gonna look for the frontier. Thanks
No english patch i guess?
Ok so take this one with a grain of salt, but possibly Dissidia? If only for the combat alone. The rest is kinda RPG kinda story telling and expoloring, but not much "hunting". The battles are on 3D maps and stuff, I think almost always 1v1. It MIGHT scratch your itch. Dont know though.
Hunting? How about the Cabela's games?