Sphinx: You there, knight. I am the guardian of this place and cannot allow you to pass without a battle.
Me: My name is Ender, Sir Ender to you. And I’m a bit weary from my long journey here, would you accept a pun battle?
Sphinx: Aye, Sir Ender.
Me: Thank you, please move aside
“not to mention” and “let alone” are both typically used with the more difficult or unpleasant things after the phrase. The main difference is that “not to mention” is usually used to bring something new into the conversation or to imply that the thing you’re mentioning needs a whole separate conversation.
“Let alone” is a way to add emphasis when denying something. Usually phrased like “I didn’t even X, let alone Y.” Y being the thing you want to deny, X being some first step toward Y or just something related that isn’t as bad as Y.
Some examples:
“Did you kill Dave?” “I didn’t touch him, let alone kill him”
“Can you walk?” “I can’t stand, let alone walk.”
The first part doesn’t even need to be a complete denial as long as it implies the second part is impossible:
“Can you run?” “I can barely stand, let alone run.”