After days of trial and error, I was finally able to successfully hard-boil a dozen eggs.

That's why I steam them. Much easier to peel. 

Use eggs that have been around awhile. Fresher eggs are harder to peel.

Boil water. 
Then add your eggs. 
Boil 12 min. 
Remove eggs and put them in a bowl of ice water for 10 min. 

This should make easy to peel eggs. 

Don't peel off the shells.  They're an excellent source of calcium, potassium, and vitamin G.
Hint - To make egg peels more palatable, cook the eggs in boiling cold water, with a tablespoon of sugar (or honey).  Boiling eggs in hot water dries the shells out. 

When you boil eggs, remove from the eye at the appropriate time and go to the sink.  Sit the pot under cold water and let the water run until the eggs are in cold water....use ice if need to.  Then take one egg at a time and roll it on the side of the sink with enough pressure to crack the shell which will also loosen it all.  This is the best sure-fire way to have beautiful eggs for making deviled eggs.  I don't but I do boil eggs for potato salad or tuna salad. This post was edited by Thriftymaid at February 9, 2022 7:35 AM MST

I do what Thrifty does, except that I don't bother with the pot - hold the hot egg in a spoon and stick it under the cold tap for a minute or two.