Unity Bot-Death Timing Question

Unity has two copies of Volatile Parts in play, and an Environment card is reducing all damage.  If she has one of her own bots shoot Bee Bot to kill it, Bee Bot's own damage occurs before its destruction of the Environment card; what about the damage dealt by Volatile Parts, though?  Is this an Order of Operations issue, or is there a fixed sequence where destruct triggers from other cards happen at a different time than ones from the card being destroyed?  (Logically, this seems reasonable; since Bee Bot has to stay in play long enough to complete its own resolution, it seems as though Volatile Parts might not "see" its destruction until after that process finishes and Bee Bot goes to the trash.)