Far out at sea, fish that live near the surface might feel some turbulence as the storm passes but most sea creatures including dolphins, whales and sharks avoid the rough surface water and swim to calmer seas.
Its a different story nearshore, changes in water temperature and salinity can be catastrophic for marine life. Hurricanes can generate massive waves which can mix warm surface water with cooler saltier water below, generating currents that extend up to 91 meters below the surface. These currents are so strong that they can sweep manatees inland into canals and ponds or away from coastal waters altogether and into the open ocean where they can become disoriented and even die.
Hurricanes also bring heavy rains where fresh water often floods areas, and because fresh water is less dense than salt water it sits on top of the salt water, just like oil on vinegar where it can prevent oxygen from reaching the salt water below, also disrupting salinity levels which can lead to sores, lesions and ultimately death in whales, dolphins and porpoises. Hurricanes can also kick up dirt and sand in shallow seas which can kill fish by clogging their gills stopping them from breathing.
See the video for a more detailed explanation of what happens to fish during a Hurricane.