To defeat Top Man, keep shooting at him while he deploys 3 tops. Those tops will fly at you, so you need to jump or slide away from your position. When you see him spinning, prepare to jump over him.
Top Man is weak against Hard Knuckle, which you will get if you defeat Hard Man beforehand.
In Dr. Wily Stage 4, you will encounter Top Man for a rematch. Use Hard Knuckle for a fast win.