The Dodonna's Pride title allows you to activate the blue crit effect of canceling all dice to deal a faceup damage. The Precision Strike objective allows you to spend a hit result to flip a facedown card. What order do these take place in? If I roll both a hit and a blue crit, can I flip a card faceup and then deal another faceup card? Or do I do the crit first, leaving me with no hit results to use?

The steps of the attack are:

1. Declare target
2. Roll attack dice
3. Resolve attack effects (here you spend the dice for the Precision Strike's effect)
4. Spend defense tokens
5. Resolve damage (here you resolve Dodonna's Pride effect)

So, the answer is that you can do both.

33 minutes ago, JJ48 said:

The Dodonna's Pride title allows you to activate the blue crit effect of canceling all dice to deal a faceup damage. The Precision Strike objective allows you to spend a hit result to flip a facedown card. What order do these take place in? If I roll both a hit and a blue crit, can I flip a card faceup and then deal another faceup card? Or do I do the crit first, leaving me with no hit results to use?

Does the ship already have a facedown damage card before you attacked? If so, you can spend a hit die (Modify Dice) to flip a card faceup with Precision Strike in step 3, and when you get to step 5, if that crit icon is still there, you can use Dodonna's Pride (Resolve Critical Effects) to cancel all attack dice to deal another faceup. But if the defending ship didn't have a facedown damage card before DP attacked, you couldn't do this.

1. Declare Target

2. Roll Attack Dice

3. Resolve Attack Effects

4. Spend Defense Tokens

5. Resolve Damage