This step is quite simple
Choose the position of your eyes. mine are vertical
Imagine a plane that intersect the egg close to the other one.
Cut along this plane with your Dremel
Be careful when cutting, you don't risk much, but your egg do.
You have to erode the shell, but not to cut the small skin under it.
Otherwise it gives freedom to the white to leak, and as the rotating tool is just over, it'll splash everywhere.
When cut enough, lay your egg on a stand made of rolled Blu-tac.
Otherwise, the egg will roll and spill everywhere.