kill the whale who caused him to have a missing leg. The rising action also includes the part of the book in which other ships cross the Pequod's path, including theJeroboam of Nantucket, on which a sailor announces that he is the archangel Gabriel. This man issues terrible prophecies to Captain Ahab, such as "Think, think of thy whale-boat, stoven and sunk! Beware of the horrible tail!" The crew of this other ship recount an incident in which the mate of the Jeroboam was tossed into the air and drowned when the white shadow of the whale appeared, while the boat was not harmed. Nonetheless, Captain Ahab pushes ahead in his quest to find Moby Dick. 

Later, continuing the rising action of the plot, the Pequod meets another ship called the Samuel Enderby of London, and a sailor on this ship tells Ahab the story of the loss of his arm to what he calls the "White Whale." The rising action also includes numerous mentions of the word "coffin," as Queequeg has a coffin built for him when he thinks he is dying (later the coffin becomes the way in which Ishmael is rescued from the sinking Pequod). The frequent mentions of the image of a coffin contribute to the rising action, as they foreshadow the death that is to follow for the ship's crew.

The climax to the story is Captain Ahab's final encounter with Moby Dick. This is the resolution of the rising action, as Ahab finally tries to kill the whale who is his nemesis and winds up causing the deaths of himself and all of his crew, save Ishmael. 

In my opinion, the climax occurs on the third day of battle with Moby Dick, when the whale rams the Pequod and sinks it. Ahab is caught in a harpoon line and dragged out of his boat to his death. Thus, Ahab’s maniacal pursuit of the white whale, which is the main plot of the novel, comes to a climax. The conflict man against nature is resolved, and man loses. While Ahab believes the unnaturally white whale Moby Dick is the incarnation of evil, Ahab’s mad obsession to pursue and kill the whale is also unnatural and turns Ahab evil.

Ahab’s men are caught in a whirlpool created by the Pequod when it is sinking and they all drown. The only survivor is Ishmael, who was thrown out of his boat earlier and is too far away to have been caught in the whirlpool. Ironically, he saves himself by clinging to Queequeg’s coffin, an item usually associated with death. Ishmael is picked up by another ship, the Rachel, still searching for its own lost crewman, whom Ahab refused to help the day before. Thus Ishmael (in the Bible, Ishmael was a wanderer because he was cast out by his father, Abraham) is the only one that the Rachel finds in the end (in Jeremiah 31:15, the prophet speaks of 'Rachel weeping for her children'). This also resolves a major theme of the novel, that God’s ways are above man’s ways, and who can fathom them?

The climax of Moby Dick is most certainly when Ahab finds the white whale and, after three days of "giving chase," plunges his harpoon into Moby's side only to get caught around the neck with the line and die as a result.  Enotes explains the climax of the plot quite well in its Guide to Literary Terms:

Climax - the moment in a play, novel, short story, or narrative poem at which the crisis comes to its point of greatest intensity. 

This is certainly true in the case of Moby Dick!  Readers have spent hundreds of pages reading about both how to whale and how this specific whaling voyage was going.  Ahab finally meets his nemesis, and the climax is at hand.

Although I am a bit confused as to what you mean by the "goal" of the novel, I will say that Herman Melville definitely had two objectives in mind.  One was to explain the occupation of whaling (embedded in there, I'm sure, was the hope that he might inspire some young boys to take up the job).  This is why there are many chapters devoted specifically to that subject interspersed throughout the novel.  Secondly, Herman Melville wanted to create an interesting story, relevant to the time, that families could read together as an activity.  This is why it was released in many numerous installments.  Families would read one installment and then anxiously await the next one (and, of course, buy it when it appeared).  Thus Herman Melville created his own type of suspense surrounding his novel.

Herman Melville's dark classic "Moby Dick" reaches its climax after many long chapters on the anatomy of whale, the abnormal and evil connotations of white, and the strange introspections of the obsessed Captain Ahab, who seeks the great white whale for revenge, but also as the key to some metaphysical answer.  For when the first mate, Starbuck tells Ahab "To be enraged with a dumb thing, Captain Ahab, seems blasphemous," Ahab replies,

Hark ye yet again--the littlelower layer.  All visible objects, man, are but as pasteboard masks.  But in each event--in the living act, the undoubted deed--there, some unknown but still reasoning thing puts forth the molding of its features from behind the unreasoning mask.  If man will strike, strike through the mask!  How can the prisoner reach outside except by thrusting through the wall?  To me the White Whale is that wall, shoved near to me.  Sometimes I think there's naught beyond.  But 'tis enough.  He tasks me; he heaps me; I see in him outrageous strength, with an inscrutable malice sinewing it.  That inscrutable thing is chiefly what I hate; and be the White Whale agent, or be the White Whale principal, I will wreak that hate upon him.  Talk not to me of blasphemy, man; I'd strike the sun if it insulted me....By heaven, man, we are turned round and round in this world, like yonder windlass, and Fate is the handspikes.  Who put it into him to chase and fang that flying-fish?  Where do murderers go man?Who's to doom, when the judge himself is dragged to the bar?

A dark Romantic, Melville perceived the dark side of Nature, a Nature working against man.  The climax comes to Melville's novel when Ahab and his ship, the Pequod, catch up to the "inscrutable malice," Moby Dick in Chapter 133:  "\

There she blows!--there she blows!  A hump like a snow-hill!  It is Moby Dick!

None of the crew win the doubloon, for it is Ahab who first spots the whale.  The whale turns as the boat containing Ahab nears, opening his mouth to tear into its side.  Ahab would stay this force of fate as he "made one final effort to push the boat out of the bite." Withdrawing momentarily from his prey, Moby Dick turns sideways and churns the water "in his vengeful wake," Ahab's head "was seen, like a tossed bubbel which the least chance shock might burst.  But, he is rescued and the second boat gives chase.  This chase lasts for a significant three days.  On the second day, Ahab tells Starbuck:

This who act's immutable decreed.  Twas rehearsed by thee and me a billion years before this ocean rolled.  Fool! I am the Fates' lieutenant, I act under orders. 

On the third day,Time itself now held long breaths with keen suspense and Ahab tells Starbuck, "For the third time my soul's ship starts upon the voyage, Starbuck." Finally, Moby Dick succeeds in killing Ahab, who having smashed the other two boats, meets his lonely death as Fedallah is seen lashed by harpoon lines to Moby Dick's flank and Ahab harpoons Moby Dick, in trying to "break through the pasteboard mask" of this creature, and Ishmael falls out.  Ahab's harpoon line runs afoul and, as he stoops to dodge it, the line is pulled around his neck.  Thus, he and Moby Dick return to the lower depths. 

Ishmael, whose Biblical name means he is meant to wander, is drawn into the vortex of the sinking Pequod; Up shoots a coffin from the whirlpool that he uses as a buoy until he is rescued.