When Bossk shoots a ship with two shields and rolls two crits, may I choose to use the ability the way that one crit will pass the shields?

Assuming that your opponent rolls 0 evades, then yes. Boosk's ability only comes into play before dealing damage and not during the modify attack dice part.

Specifically:

After all the dice have been compared and the evades have cancelled out hits/crits, if two crits remain, before damage is dealt, Bossk's ability triggers, converting one of the crits to two hits.

Then damage is dealt as hit/hit/crit, and the enemy takes that damage as normal.

I think I see another point worth clarifying in the question - Bossk's ability can only trigger once per round, for one crit. So if you rolled two crits, you're looking at, at most, 3 damage (hit hit crit) and not four (hit hit hit hit).

I think I see another point worth clarifying in the question - Bossk's ability can only trigger once per round, for one crit. So if you rolled two crits, you're looking at, at most, 3 damage (hit hit crit) and not four (hit hit hit hit).

Point of order: Bossk can only trigger once per attack. If you perform multiple attacks in a round, such as with Cluster Missiles, you may use his ability during each of those attacks.