Newborn dolphins never sleep and always keep one eye up. Half of a dolphin's brain is awake while it sleeps. To rest their brains, they switch sides.
Orca infants spend their first few months without sleep. Calves need to move continually to keep warm. Once they have blubber, they can rest and sleep.
Bullfrogs react to stimuli as though awake even when sleeping. Brumation is like binge dozing after no sleep, according to some. In other months they "relax" yet never sleep.
Bluefish, often called snapper or tailor, migrate along the Atlantic coast seasonally. Migrating fish rarely sleep. Even when resting, bluefish swim ceaselessly and respond to stimuli.
Fish sleep differently when caring for young or after birth, in addition to migrating. Tilapia are awake and active for 22 weeks after birth.
Assume sleep involves brain inactivity. Without brains, upside-down jellyfish can't sleep. Instead of a brain, they have a network of sensors and tentacles to feed.
Butterfly torpor instead of sleep. Torpor has a low body temperature and slow heartbeat. They relax with eyes open among leaves or upside down on twigs.
Walruses look sluggish, but they can stay awake for 84 hours. They'll swim and hunt for food. Walruses make up for lack of sleep with long naps.