Direct answer: Penguin Smash runs from November 4 at 07:00 UTC until the November 18 maintenance. Complete event missions to earn Penguin Smash Event Tickets, then use them in the event for limited rewards.
Who can enter Penguin Smash?
The official requirement is completion of the Main Quest “Calm Days”. The event notice lists mission phases I–VII and a maximum of 343 Penguin Smash Event Tickets from completing all listed missions.
What rewards are listed?
The official reward table includes Gold, ingots, Remnants of the Rift, Tailor's Stitching Needles, Engraver's Fabric Scissors, Platinum Ingots, crafting ornaments and Accessory Crafting Blueprint Selection Chests. Limited rewards have stated maximum quantities in the official table; check the in-game event screen before spending tickets.
Rewards and mission tickets must be claimed within the event period. The notice does not establish a banner rate, pity rule or character ranking.
Official source: Penguin Smash!.
Events schedule · Update Eve Check-In · November 5 maintenance