Possible Clues:

• An arctic toothed whale
• Sea mammal
• Warn Henry about the monster of sea
• Whale with tusk
• What's found primarily in North Atlantic region with horny appendage (long)
• Somehow warn Henry there's a creature in the sea
• Cetacean with large tusk
• Wrongly warn Henry about large sea-creature
• Wife managed to get around Falstaff's fellow-drinker, a beast
• Sea creature with a long spiral tusk