Hint: Bypass areas:
When on a stage made up of many vertical levels, look for holes in the ceiling. By repeatedly wall jumping, you can jump through these holes and bypass entire sections of the stage.
Hint: Extra points when facing Bosses:
On the level where you take on a succession of Bosses, you can increase your score by letting the last Boss kill you, then going back to the start of the level and going through again. You will not run out of lives because you will keep getting the extra life from the sheer amount of points you are getting. You can do this as many times as desired.