i have not played Dodonna much, but i was thinking, with his ability and mine fields.

DODONNA ABILITY:

Before an enemy ship is dealt a faceup damage card, look at the top four cards of the damage deck, place one on top of the deck and discard the others.

so, if the objective is "mine fields" then if a face up damage card is dealt from a mine, then the enemy player of Dodonna would have to present 4 cards to choose 1 as face up?

Correct. Dodonna's ability has no further constaint about it having to come from an attack you make.

So minefields could trigger it, as could, for example, overlapping an asteroid.

Agreed.

All times that an enemy ship is being dealt a face up card, Dodonna triggers, as long as he is on the Table...

This includes, and is not limited to, Ship Attacks with Criticals, Bomber Attacks with Criticals, Asteroid Impacts and Minefields.

One of the few times it does not trigger, of course, is when a "HIT" is spent with the Precision Strike objective. The Face Up card is not being dealt at that time, its simply being turned over from a face down card.

Interestingly, and for added context, in an early preview of Armada Dodanna explicitly only let you select from (3 at the time) face up damage cards when you dealt a critical hit - the wording was clear.

By the time the game was released they upped it to 4 cards, and removed the requirement that you actually have to deal the critical.

If an opponent takes a face up card for any reason, you get to look at the top 4 and pick it.

Interestingly, and for added context, in an early preview of Armada Dodanna explicitly only let you select from (3 at the time) face up damage cards when you dealt a critical hit - the wording was clear.

By the time the game was released they upped it to 4 cards, and removed the requirement that you actually have to deal the critical.

If an opponent takes a face up card for any reason, you get to look at the top 4 and pick it.

That was in the day when ships had 3 Anti-squadron dice.