The vast majority of shots should involve camera movement. Whether the camera shakes, pans, tilts, dollies, whatever, a fight sequence with stagnant shots looks unrealistic.
The two characters should occupy a large portion of the frame. You want to convey that this fight is taking place in their own little world. Showing oodles of background takes away from the intimacy.
Film the entire fight from three master shots: one with both of them in frame, one looking over the shoulder of Character A and one looking over the shoulder of Character B.
You will not use the entirety of these shots when editing, but they will be there to revert back to at all times. The camera again should be moving throughout these shots.
Film closeups of all of the actual fighting-a closeup of a fist clenching, one of the punch hitting the jaw, another of a punch connecting with the stomach.
We don't need to see faces too often once the fight begins, but rather limbs flailing. If Character A starts kicking B, we need not see his face, but rather his foot connecting.
When editing, utilize all of the closeups but edit them in quickly. With all of the camera movement and quick cuts in editing, a seemingly simple fight will come off extremely dramatic.