Quick Man is very... quick. His weapon is the Quick Boomerang which he throws in 3's & homes in on your position. His room is not leveled but you can use these to evade his charges. Even a veteran player may still get damaged when battling him so its advisable to save an E-tank or two.
Quick Man is weak against Time Stopper, which you will get if you defeat Flash Man beforehand. This will deplete Quick Man's energy in half. It is best to use it after you deal him half of his energy.
Quick Man is also weak against Crash Bomber, which you will get if you defeat Crash Man beforehand. You have to take on damage to use the weapon effectively. Wait next to the wall you started in & plant a bomb on it. Let him give you damage so he will continue running towards the wall, then the bomb will give him 2 to 3 hits. Try using the rooms terrain to get him trapped & bombard him. Hitting him directly with the weapon doesn't significantly damage him, but its explosions will.
In Dr. Wily Stage 4, you will encounter him again for a rematch. His room this time is leveled. Damage him until his energy is in half then use the Time Stopper. If possible, save the Crash Bomber for Wily Machine No. 2.
Oddly, when Quick Man gets hit with a weapon that bounces off his body, he gets stunned for a few seconds.