Today we were practising a simple routine, blocking a slap to the head and then delivering a punch to the sternum. At one point the teacher stopped me and my partner to demonstrate. He told us that we may just have been blocking a "slap", but then he showed us how there are different levels of slaps - he used the base of his open hand to just lightly tap my jaw and said, "A proper slap will break this." And I could feel that small movement make my entire jaw bone shift from side to side.
It reminded me of my old Tae Kwon Doe teacher showing us a pattern in which one of the moves was a specific punch delivered at a certain angle and a certain point so as to make the target void his bladder. That's how specific martial arts get. Traditions stretching back thousands of years, perfecting the art of killing people.
Now, in the West we have lost those traditions, although WMA and and HEMA people are doing their level best to reinvigorate them, but there's no reason why in a fantasy world that would have happened. Those martial traditions would be unbroken and ancient. Doesn't it seem likely that in such worlds, martial arts schools would have developed teaching to teach people how to kill not just other people, but also orcs, trolls, ogres, giants, dragons, etc.? Here's how you jab a spear just so that it ruptures a hill giant's spleen. Here's where an orc's jugular vein is - different to humans, slightly to the left. Here's the spot to hit if you want to make a dragon shit itself...
In view of, this, I give you the experimental Jack the Giant Slayer Rule.
At character creation, the player of a fighter can specify that his PC has received training in how to fight a certain type of monster or humanoid. From that point, once per combat, the player can elect to do double damage against that creature type, but he must declare this before rolling to hit.
A fighter may undergo specific training for killing other types of monsters and humanoids every other level.