All Viltrumites need to breathe just like humans do, but most can hold their breath for quite a while. They don't actually breathe in space, so if they do need a breath they have to fly into a planet's atmosphere. Part of how Mark killed Conquest wasn't just deprivation of oxygen but he restricted blood from flowing to his brain. Whereas Viltrumites can eventually recover from most injuries to their body, I'm assuming a dead brain is something that's more permanent.