This came up in a casual game today - can Boba Fett be used on a ship with Integrated Astromech? I got a crit through onto my opponent's Poe with IA and R5-P9 via a proton torpedo, and decided I wanted to disintegrate the droid, to prevent Poe running away and regenning. Afterwards, I realised that he ought to have been able to IA the crit. It didn't affect the outcome of the game, but I'd like to confirm for future reference:

The timing on the cards seems fairly clear: Boba happens after the attack, IA happens after a card is dealt, so IA should trigger first. If my opponent forgets IA, or chooses not to use it, I'm clear to burn the droid. But if he does use IA, does that crit still count as having been dealt, so I could disintegrate something else if I wanted to? Or did discarding it mean that it no longer counts as having been dealt, and thus Boba doesn't happen?

OK so it goes like this:

BOba's ship deals a face up damage card, triggering his effect. It doesn't matter what happens to the card afterwards, as long as it was initially dealt face up.

The X-Wing can choose to trigger IA, discarding both it and its astromech in order to discard the face up damage card.

After the attack, Boba's effect resolves, regardless of what happened to the card and to the astromech. If any upgrade cards are left on the x-wing, he can remove one of them. If the x-wing chose not to trigger IA, Boba could then discard the astromech, rendering IA no longer useful. If the x-wing discarded IA and its astromech and is left without any cards as a result, Boba is SOL and cannot force the x-wing to discard anything, but he can be saved to be used later should his ship deal another faceup card.

Boba is a trick guy when it comes to discarding thing the target ship may discard.

If you shoot a ship with IA and an Astromech and would be dealing it a face-up card its owner has a choice: Either discard the Astromech and cancel the incoming face-up card or do nothing and then see what Boba Fett will do. If he chooses to do nothing then Boba would have the option of stripping of that Astromech himself (making IA useless), stripping off some other upgrade, or just not doing anything and sticking around to see what else might show up.

These same questions happen when a ship with Chewie as crew is dealt a face-up card. Boba will get the option to take away an upgrade although if Chewie is still there when he does he can take the Wookie without the Wookie doing anything.

If you think about it Boba can be a good way to force players to spend discard effects early instead of letting them sit back and wait on them so they can be used at the best possible moment. With AI that typically means you only pop the Astromech when it is going to save the ship from certain destruction. With Chewbacca is usually means either waiting to stop some nasty critical hit or to avoid the hit that will cost points and/or finally destroy the ship.