At the end of World 3-4, you'll encounter a boss in which you fight in the foe's stomach. If you do not move left/right at all on entering the stomach, you will never be hit by the acid. Furthermore, try to angle your egg shots to hit the sides of the uvula at the top of the screen: for reasons unknown, hitting the target from the side, as opposed to just aiming straight up at it, does significantly more damage.