First off, card for reference.

Second, this is assuming you can use the shields from the Escape Craft to absorb damage against the carrier ship (a point @meffo debates against :P)

Situation: The YT-1300 carrier ship has no active shields. The Escape craft has 2 active shields, and is docked with the YT-1300

Question: You suffer a [Hit] and a [Crit] damage. Can you suffer the [Hit] first to the carrier ship (drawing a damage card), then choose to use a shield from the Escape craft to absorb the [Crit]?

Why or Why not?

Damage is assigned and dealt with individually so yes, if meffo is incorrect spending shields on the docked YT-Dart.

it's worth noting that that's the RAW argument. loosing is not spending, even if spending is loosing. i believe the intent is for the player to be able to use the shuttles shields even while loosing them, it's just not what the card says. when i've organized small tournaments, i've clarified this ruling beforehand. it's worth noting basically no one ever flies the ship anyway, especially in a competitive setting, since it's really bad. FFG done goofed big time when the set its primary attack value to two instead of three, even if it maybe makes sense thematically that the modified and salvaged versions of the craft have upgraded weapons systems.

if you could use the shuttles shields for taking damage, it's clearly a may statement, meaning you get an opportunity to use the ability every time you would loose a shield. that would mean you can take hits to the hull of the falcon and use the shuttles shields whenever a crit shows up. even during the same attack, since damage is always dealt one at a time. i'd say it's almost always better to use the shuttles shields earlier than that to try and avoid getting halved, but still.

i guess this is a list, but the title is pretty much never worth it. maybe you want to do something fancy with outer rim pioneer in the shuttle constantly docked and use the title with a bunch of mining guild ties, qi'ra or what not. seems not worth it, but could be fun. also this list sucks, since the jumpmaster has a bad dial and the falcon is just a bad ship in general. you'd probably need a bigger bid with a list like this one as well. with such bad reposition options, i6 is rarely worth it anyway.