Start by boiling your eggs.  There are several methods you can use; just stick to whatever works best for you.

Allow the eggs to cool and crack them all over.  FYI, it’s okay if there are pieces missing.

Add just enough water to your cups to cover the eggs.

Add food coloring to each cup.  I added about 6 drops.

Drop one cracked egg into your cups and allow it to sit for a few hours in the refrigerator.  The longer you can let them sit, the bolder your colors will be.

Remove the egg from the cup, peel off the shell, and enjoy your fun hard-boiled dinosaur eggs.