Don't skip the step with ice-cold water. Shocking the eggs with such water will make the whites shrink just enough to separate them from the shell. Also, try to peel the eggs directly into the bowl with water. This will allow the liquid to seep under the thin film, which, in its turn, will help release the shell. Very fresh eggs don't peel as easily. So it might be better to buy the eggs in advance and let them sit in the fridge for a couple of days.