However, it was revealed by Vril Dox that Despero was not killed - quite the opposite, in fact. As you can see, not only is his mind still fully functional (as nothing but a head), but he is/would be capable of fully regenerating the rest of his vessel:
Not only does a blast from Despero bring Starro the Conqueror to his knees, but had Despero acted immediately he could have killed Starro by himself (via skull-crush):
It was also revealed that Despero's 3rd eye makes him immune to both the powers of a Starro-starfish, and the Conqueror's high-level TP (very impressive):