While hitting the punching bag, use combos and not speed hits. Mix it up with left and right punches that are both high and low. A great combo is left normal, right normal, left normal then right low/uppercut. Usually that will wipe a new bag out immediately.
When dodging the balls, keep you hands together to the point where they touch. Then, move just your hands and not your body to dodge the balls. This will both keep you from tiring out as well as make your character move faster. Also, when the trainer throws two balls, make sure you let only one hit you.
When you must hit the trainer's target gloves, do not swing hard or fast. You'll just get penalties for hitting him. Make slow controlled hits to score higher in the long run.