The big ghosts can be killed with a single egg shot by shooting them as they are scrolling on screen.
More eggs should probably be gathered than shown in the video below, to be safe. Green pirahnas normally require 3 shots to be killed, but they can be safely passed through for a brief period after being hit. Exploit this to get past the green pirahna at the end of the level with only one egg. A safe method of getting the quick kill "Oh my!" on the boss is to go all the way into the boss room and stand on the edge of the ledge. As long as you do not go too far in, the boss fight won't trigger.