Ermmmmmm, you can't kill insect eggs
or pupae for that matter. Both have a hard shell that is impermeable by insecticides.
Insecticide kills adults and larvae
I use Nylar, which is a growth inhibitor. After thorough vac/clean, all likely areas are sprayed (as detailed above). This means that any larvae hatching from eggs come into contact with it and are stopped from reaching the next stage of the life cycle.
It's virtually impossible to remove eggs by cleaning, either vac or extraction, so this is the best way of dealing with the problem.
Works on beetles and moths just the same.