Complete final stage on the Hard difficulty setting.
You only need to get through level 15 on Hard, so upon completing Story mode, select level 15 and put it on Hard. You got 24 lives and 4 power-up spheres in the room. Use your special attacks on the big bosses and make good use of the spheres to replenish your health and get 2 special attacks. Use the red orb to give more damage to the bosses.