Taking 1 damage
It removes a shield if the ship you're attacking doesn't evade all damage and has shields remaining.
You would then perform the attack a second time, again removing one shield if your attack hits and they have shields remaining.
If they don't have shields, or none remaining, the attack will deal a facedown damage card for each attack that hits.
Shield if they have shields.
Cards are only dealt under shields if the thing causing the effect specifically says to deal a (faceup or facedown) damage card.
But, note, the defender still gets to roll green dice; only if their evades are less than your hits and crits, do you hit and then cancell all dice and do a damage.