From RitR:

I would read that as in addition to? IE., I take my shot at your ship with an ACM-Demo, as second player, get 4 hit/crit results for 8 total damage with crit effect. I resolve my ACM crit first and you lose 1 shield from each of the 2 adjacent hull zones, and then eat/resolve 8 damage. Also during that attack, since you are at distance 1 of an objective, I 'resolve the following critical effect' of doing 2 more damage to you from the Volatile Deposits objective.

The card doesn't seem to say it adds this crit effect to the attack (which I would understand to mean that it becomes one of the options - IE., I could take this crit effect or ACM or the standard crit). Rather, it just says to resolve this while attacking , suggesting it simply occurs alongside everything else that happens.

Thoughts?

https://starwars-armada.fandom.com/wiki/Critical_Effects

The attacker can only resolve one critical effect per attack. I don't see this objective making an exception.

Also, I think in your example above, the enemy ship would suffer two extra damage, not four extra.

Edit: That being said, it's each ship/squadron at distance 1 of the chosen obstacle. So if some poor soul chose to park half his squads on the station, it may be worth skipping ACM.

Let's break down the full special rule, not in piece meal.

Quote

Special Rule:
While a ship is attacking a ship, the attacker can choose 1 obstacle at distance 1 of the defender, then resolve the following critical effect.
Blue Crit: Each ship or squadron at distance 1 of the chosen obstacle suffers damage equal to half of the total number of crit icons in your attack pool, rounded up.

If the defender is one of the first players ships, the attacker can resolve this effect with any crit icon.

You can only choose to resolve one critical effect in the resolve damage step.

"While a ship is attacking a ship, the attacker CAN choose 1 obstacle at distance 1 of the defender, then resolve the following critical effect."
So the first part is, you can choose 1 obstacle at D1 of the defender. If you do, then you gain access to resolve the critical effect that is granted with the special rule.

For the 1st player, they must roll a blue crit to trigger it, for the 2nd player, any crit icon will do.
Once past the "Spend defense tokens step", and you've reached the "resolve damage step" at that point in time you CHOOSE which critical effect you are resolving, the objectives, or another effect you are able to trigger.
If you have Fire Control Team, you could exhaust it at this time to trigger both another critical effect.

Keep in mind, Damage control officer can CONTAIN this critical effect just like any other critical effect.

9 hours ago, Bertie Wooster said:

So if some poor soul chose to park half his squads on the station, it may be worth skipping ACM

If there were one. If anyone does that with an asteroid they deserve exactly what they get. 🙂