An old issue of Nintendo Power did a damage analysis of the home version on attacks and damage:
A basic attack (i.e., one normal strike) will do two (2) points of damage. A jump kick (i.e., jump then attack) will do three (3) points of damage. A special attack (i.e., jump and attack together) will do four (4) points of damage.
Most enemies met early on will have three hit points, making them easy to kill with jump kicks. Other stronger enemies will have hit points as a multiple of two or three. By counting the number of attacks needed to down an enemy, you can estimate its hit points.