Say I have a creature with two "On destroyed" triggers that appear to have mutually exclusive instructions: "archive that card" and "put that card on the top of your deck". Which one will be resolved on this creature's destruction?
Active Player (AP) chooses.
Whenever there are multiple effects to resolve, the AP (whose turn it is at the moment; this may or may not be the owner of the card/effect) chooses the order to resolve the effects.
In the example scenario, whichever effect the AP chooses to resolve first will be the final result. I.e. AP chooses to resolve "Destroyed: Archive" first > the card is now archived > "Destroyed: Place on top of deck" never happens because the card is no longer on the field.
The above actually means that if a card has the lines "Destroyed: Archive" & "Destroyed: Steal 1 Amber", AP can actually decide if the steal happens depending on whether they resolve Archive first or second.