The actual two parts into which Lee divides her novel consist of the time leading up to the trial and the trial with its ensuing events. If you need the climax of those two parts, the climax of the first is when the children begin to change their view of their father. In Part 1, Scout and Jem see Atticus as old and boring, but a series of events helps to change their perspective. They find out that Atticus is a great shot, get their own air rifles for Christmas, and most importantly, as the events leading up to the trial heat up, they begin to see their father as the man of honor that he is.
In the literal Part 2 of the novel, the climax is when Tom Robinson is found guilty and killed soon afterward. Everything that Atticus has worked toward and that his children had hoped for seems to be lost at that point. Of course, this is where critics disagree over the novel's turning points because many see the book as having two unofficial parts--the story of Boo Radley and the trial of Tom Robinson. If that is the case, then Tom's fate is the first climax, and Boo's rescuing the children is the second.
The connection between the two parts is the Tom Robinson/Bob Ewell conflict. If Bob Ewell and Mayella had not falsely accused Tom, then the trial would have never occurred, and there would have been no need for Bob to attack the children or for Boo to save them.
You will need to decide if you want to address Harper Lee's literal two parts or the natural two parts of the novel in order to determine the climaxes.