I am assuming that someone who hunts down Bounty Hunters is on the wrong side of the law.
Names for gangland/underworld killers, whose activities may include getting rid of bounty hunters could be
Plugger
Cleaner
Eliminator
Enforcer
Butcher
Slayer
or you could go for an animal motif, but this means 'creating' a term for the role you have in mind
Wolfshead (medieval term for an outlaw)
Jackal (as in the film 'Day of the Jackal')
Coyote (NA Indian tradition)
Hellhound
or some bird of prey, or a large cat.