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.