Major improvement to first world due to use of a better weapon. Also did second and third world.
Near the end of the third world, I was forced to pick up an inferior weapon ("fire swing"?) to get through a floor of breakable blocks. I took time to replace it with a slightly better weapon later ("beam"?), without which the boss would have been a major timesink. However, this weapon is not as strong as the weapon found in the second level of the first world ("big punch"?). Therefore, there's a possibility that it might be faster to do the last normal level of the third world before getting the "beam", but I don't think I actually lose time by using it in this level.