Mangler would change the results before you actually deal the damage cards. So:
Boba rolls attack dice and get three hits.
3 hits become 2 hits and a crit due to the Mangler. During the modify attack dice step.
Khiraxz rolls defense dice and whiffs.
Hits become damage during the compare results step.
First damage removes the shield token.
The second damage is turned face up due to Greedo's ability, and any effects are resolved.
The crit is dealt as a face-up and any effects are resolved.
Ultimately, do what the card says to do... don't do what the card doesn't say to do.