Can Bossk's pilot ability trigger on both attacks? I imagine it could but, looking for confirmation. Thanks.

It seems like it should. There's no limit to how many times you can use it. It simply says after an attack hits so if you hit both times and have an uncancelled crit both times you can use it twice.

Yeah there are no 'once per round' or 'primary attack' clauses, so I'd say it works.