When you score an automatic hit like in a duel or via a spell against a "Hard to Kill" chart, is that a roll on the chart, or do you still need two automatic hits to roll once against a resilience 2 unit/figure for example?

You'd still need 2 hits to get past 2 resilience, 3 to get past 3 and so on. Only exception is if you have a special rule that reduces resilience or causes a casualty regardless of resilience.

Example for the first one might be: Legolas using his Crippling shot on a monster first and then making an Epic Shot. Crippling Shot reduces a monster or flying monster's resilience by 1 (to a minimum of 1)

An example of the other type might be: Boromir uses Mighty Blow and then wins a Duel. Each hit he scores while rolling on the Heroic Duel table will cause a casualty regardless of resilience because of Mighty Blow.