One of the main reasons it's hard to get the shell off a hard-cooked egg is its freshness. The fresher the egg, the harder it will be to peel. I know it sounds crazy, but it's true. Placing the eggs in an ice water bath will also help remove the shell. The ice bath stops the cooking process and shocks the egg white, causing it to shrink back from the shell, making it easier to peel. Peeling them right away (while in the ice bath) will also make the process easier. Cracking the shells while the eggs are submerged allows the water to flow into the space between the egg white and membrane, helping to separate them.