Much of building the ability to hit hard is being proficient at whatever martial style you practice. That having been said, all styles rely on the same base of power generation to hit hard. The power starts with the hips, relaxed movement for speed and dynamic tension at the follow through for delivering the most skull-crushing blow. This is true for boxing, or Kung Fu or karate styles or Muay Thai or Russian Systema which uses a circular “power slap” kind of a blow. All power is transferred from the feet up through the legs, hips, back and abs. These are the martial arts exercises that may give you the most capability for the areas of your body in the most martially applicable way. It’s your decision to become technically proficient at whatever form of punching you use to make the maximum of it.
The one-arm dumbbell press. There are multiple styles of the one arm press done with a dumbbell from strict to explosive. All styles will help because they all overload the body in a way to unify it behind one limb which is a key in hitting. Putting your whole body behind the hitting arm. This will reinforce your chest and shoulders better than any other exercise as well as teaching unified movement of the upper back and coordinated movement of the core and legs.
Full Squats or Deadlifts. If you’re truly going to learn to hit hard you have got to be doing full body exercises. The kind that makes your body function as one piece and adds to the power of each muscle in the whole body, not just some isolation exercise. Maybe not everyone prefers squats like I do but one or the other is an absolute must for building an extension of the posterior chain to generate real strength for hitting.
The kettlebell swing. This drill gives you not only explosive, extending power of the hips, legs and back, but endurance to boot which is a massive benefit in any sort of punching style. Desire is everything in lifting. Something that is huge on the slate for super self defense experts like Steve Cotter. When you do the swing think not only of crisp, snappy, strongly explosive movements, but of the same potent body extension that you would use in throwing a strike. Breathe deep. Deep breathing increases your chi as well as vitality.
Working these three exercises into your routine will not only explode your conditioning, but will teach your body the right movements and sort of ability to make you hit more powerfully than previously. There are some systems in here that mixed in your total program will give you hands of might and the power to follow through with.