Etahn: When an enemy ship inside your firing arc at Range 1-3 is defending, the attacker may change 1 of its hit results to a critical result.

vs

Elusiveness: When defending, you may receive a stress token to choose 1 attack die. The attacker must re-roll that die.

My opponent believes the re-roll can allow him to change another existing (or re-rolled) hit to a crit as Etahn's card does not say 'Once per round' or 'once per attack';

whereas I viewed it as once per attack, as explained in an answer on this thread: https://community.fantasyflightgames.com/topic/200235-etahn-question/?hl=etahn

Can someone please correct my opponent or me?

You're correct, Etahn's ability triggers once per attack. The trigger for his ability is "When an enemy ship [...] is defending," which lasts for the entire attack. And the once-per-opportunity rule means that he can't activate multiple times in the same attack. See page 8 of the Rules Reference:

A card ability cannot be resolved more than once during the timing specified on the card. For example, a card with the timing of “when defending” cannot be resolved twice by the defender during a single attack.

Elusiveness doesn't create a new attack (it's just a modification of the attack roll, same as Etahn's ability), so it doesn't generate a new opportunity for Etahn.

Pandademic is correct. Also note that the defender modifies the attack dice first, so the defender has to decide if they want to use Elusiveness before the attacker decides if they want to use Etahn.

^