Minecraft wiki entry for Monster_Hunter, associated text: Achievements#Monster Hunter, an achievement for killing a hostile mob or one of the following neutral mobs: enderman, zombified piglin, spider, cave spider.
Advancements#Monster Hunter, an advancement by killing one of these 34 mobs: Blaze, Cave Spider, Creeper, Drowned, Elder Guardian, Ender Dragon, Enderman, Endermite, Evoker, Ghast, Guardian, Hoglin, Husk, Magma Cube, Phantom, Piglin, Piglin Brute, Pillager, Ravager, Shulker, Silverfish, Skeleton, Slime, Spider, Stray, Vex, Vindicator, Witch, Wither, Wither Skeleton, Zoglin, Zombie, Zombie Villager, Zombified Piglin.