What is the order of permanents destroying via "Destroy Them All!"?
Backup Copy will work. From the rules:

Page 10
DESTROYED
When a card is destroyed by a card effect or when a creature has damage on it equal to or greater than its power, that card is tagged for destruction. After it is tagged, then that card’s “Destroyed:” abilities trigger, and finally the tagged card is placed into its owner’s discard pile. If multiple cards are simultaneously tagged for destruction, the active player chooses the order in which to resolve the “Destroyed:” abilities of any of those cards. All the tagged cards are put into their owners’ discard piles simultaneously, and the active player chooses the order in which those cards are arranged in their owner’s discard piles.

So as per &quot;Card Abilities&quot; (page 7), we resolve Destroy Them All in the order it's written. First an artifact is chosen (if possible), then a creature (if possible), then an upgrade (if possible). When each one is chosen, it is marked for destruction and its destroyed abilities are triggered. None of them are actually destroyed until all have been marked and triggered any destroyed abilities.