An X-wing with 1 shield and 3 hull takes 2 damage. 1 hit and 1 critical hit.

Will the critical hit be resolved first (used on the remaining shield) or will the normal hit eat the last shield and leave the critical hit for some serious hull damage?

Normal hits are resolved first and then Critical hits. Pg 15 of the rulebook covers this in detail. In your example, the X-Wing would lose the remaining shield and then be dealt a face-up damage card for the critical.

Jim

Nice! Thanks for the answer

Regular hits get cancelled/resolved before Critical hits.

The one exception to that is if a ship is hit by an Autoblaster's attack. It may cancel critical hits before regular hits but then it's regular hits can not be cancelled by dice; if a critical and a hit both get through the regular hit will still hit first however.