Stronger enemy foes require a special attack to be downed for good, so attacking lesser foes with combos will build up the attack meter for the necessary power (the above point works well for this). This will not only defeat the most basic foes quickly and efficiently, but it will also build up the attack meter at a rapid rate, creating a special attack possibility after three or four kills. When fighting with regular foes with a sword, the best combination attack to use is a sword stroke, punch, sword stroke.
Although this seems like an odd thing to worry about, many useful techniques are taught here, which can be tough to figure out in the heat of the game.