Possible Clues:

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