This character is a hunter.
Hunting is the practice of pursuing any living thing (usually wildlife) for food, recreation, or trade. In present-day use, the term refers to lawful hunting, as distinguished from poaching, which is the killing, trapping or capture of the hunted species contrary to applicable law. The species which are hunted are referred to as game and are usually mammals and migratory or non-migratory gamebirds.
Fictional hunters on the other hand are known to hunt anything from animals to humans to monsters...