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Phantasy Star Portable 1 & 2

Phantasy Star Portable 2 is longer and better than 1 I think. You could probably play 2 without 1 but both are good games. Been a long time since I've played either so I'm not 100% sure on if you have to play 1 first. But it's better to play 1 first if you wanna play both, otherwise it'll feel worse than 2, less customization and stuff. I think both have got lots of optional missions and stuff to do, not just the story. Also if you managed to find a new copy or an unused code, you can get Wi-Fi multiplayer on Phantasy Star Portable 2 and do missions with other people.

The RPG im suggesting isnt for PSP or DS but try Zenonia its on google play store
That is one of the best mobile rpg ever

I'm not yet certain about any DS games that you are looking for but there's a PSP game that's exactly fitting your description of being both an RPG and having only one character. The game is called Gurumin: A Monstrous Adventure. It's about a girl named Parin who befriends a town full of friendly monsters, one day evil monsters called Phantoms attack, where they ransack and abduct the monsters, and it's up to Parin whose armed with the legendary drill... yes her weapon is a drill that's legendary to save her pals.