Thank you, "Mario's out for revenge!" sounds like what I'm looking for.Does "bramare vendetta" imply only that a person wants revenge, or that a person is actively seeking to take revenge? If it's the former, then "want" is the most natural way to say it--unlike YLR, I'd be more likely to use "revenge" rather than "vengeance": "I want revenge! Mario wants revenge!"
If the person in question is actually doing something or planning to do something to take revenge, you could say "Mario's out for revenge!" or "Mario's after revenge!"