It seems to me that you will need one long sentence in the opening paragraph in which you specify what two things you intend to compare and contrast. Then in your second sentence you might want to suggest the ways in which the two things are similar, and in your third sentence you might want to suggest the ways in which the two things are different. Since you say that your paper focuses on the differences between two characters, you might conclude your opening paragraph simply by saying, in so many words, that your paper will focus on the differences between the two characters. That would take four sentences. You can start your next paragraph by discussing the similarities and save your discussion of the differences for the third paragraph.
I don't think there is any set rule about how many sentences should be in the opening paragraph of a compare and contrast essay, or in any other essay. But you have to explain what it is that you are going to be writing about and what it is that you intend to prove.