Emperors are the only animal that breeds on the sea ice itself, through the Antarctic winter, and they are the hardest of the seven southern penguin species to reach. Colonies sit far south on fast ice, so seeing one usually means either a Weddell Sea voyage in November, when the ice is still solid enough to land on, or a flight-supported trip that puts you on the continent directly.
Chicks hatch around July and are still huddling in crèches when the first ships arrive. By late December most have fledged and the colony breaks up, so the window is genuinely narrow — this is one of the few Antarctic sightings where the month you choose decides whether you see it at all.