That's a "hit."
With criminal organizations (like mafias or gangs), when someone who runs the organization makes the decision to kill someone (for a wrong against the organization), that's "putting out a hit on ______." When the person is actually killed, they have "carried out a hit on ______." When the murder is described in the papers, it will be described as a "Mafia-style hit" or "a gangland hit."
I would use "vendetta" for something more personal; not something entwined with a criminal organization in place, but more if Jane (someone who isn't connected to a gang) wanted revenge on a bunch of people and went out getting it.
Most of the other words mentioned (e.g., payback, retribution, retaliation), I might use as the reasons behind the action - but none of them fully express "there's a dead guy in the street."