What does the sentence "He could have hardly been less like my boss" mean? I know I am in the realm of the "double negative" or "figure of litotes" construction but still can't figure out its meaning. Thanks.
It means he is nothing like your boss
The word hardly is a tricky word that has different meanings. In this sense it means "not", but in a way that's emphatic. It's more accurate to say that it means "certainly not" or "absolutely not". See how this shows emphasis?
Let's try making this substitution. He could certainly not have been less like my boss. I think the meaning becomes clearer now. It means that he is nothing like your boss. If your boss is lenient, then he is strict. If your boss is nice, then he is mean.
It's a colorful (perhaps ironic) way of saying this
It's worth pointing out, the mood of the sentence is subjunctive. As an exercise, let's convert your sentence to the indicative. He is nothing like my boss. Simple, right? Ask yourself why a native English speaker would use the subjunctive (and double negation) to say the same thing.
Similar to "I couldn't care less"
This phrase is similar to the expression "I couldn't care less". To say I couldn't care less means that I care so little I could not imagine myself caring less. In your example, the man is so unlike your boss that you cannot imagine him being less like your boss.