The allusion here is to boxing. It was customary for the boxers while training to strike out at an imaginary adversary merely for exercise. This was “beating the air.” The text may refer to this, or to the efforts which, when the real contest took place, each made to avoid the blows of his adversary, so that these blows should fall upon the air. The apostle struck real blows at a real adversary.
The “beating” was done by means of leather bands which were fastened around the arms and wrists, and were sometimes studded with nails and loaded with lead or iron. This made the blow heavy, and frequently dangerous. Fighting in this way was “resisting unto blood”; this is the ground of the image in Hebrews 12:44Ye have not yet resisted unto blood, striving against sin. (Hebrews 12:4).