How do you unlock Minato in Naruto Shippuden Ultimate Ninja Storm 3?

It really depends on what game you're talking about. I can't help you a lot, but if you're referring to either UN3 or UN4 (Ultimate Ninja 3 or 4), then I can tell you.

For UN3, I believe all you have to do is get all of the other characters. Either that, or you complete the game (most likely the latter of the two). I'm sorry to say that I haven't played that game in years, so I don't know the correct answer.

In UN4, however, all you have to do is finish the Flashback Arc, or whatever it's called. Collect all of the Memory Pieces, play them in Hero's Mode, and you're done.