What are the most important chapters in part 2 of To Kill a Mockingbird?

I would agree that chapters 20 and chapters 28 are the most important in part two of the novel, but I would also add chapter 29.
Although we are told from the start that Tom Robinson will never be acquitted of raping Mayella Ewell, Atticus mounts a strong and convincing defense, so persuasive that we can even hold out hope that the jury will do the right thing. When they don't and instead convict Robinson in chapter 20, despite all the evidence in his favor, it is a defining moment in the novel.
Chapter 28 is also a defining moment, for Bob Ewell's attack on the children brings us back to chapter one and Jem's broken arm—the beginning that set the story in motion. Now we find out why Jem has a badly broken arm, as well as about the knife attack on Scout.
Chapter 29 is also important because it is there that Scout identifies Boo as the one who saved her from Bob Ewell, saying, as she points at him in the corner,

Why there he is, Mr. Tate, he can tell you his name.

One could argue that chapters 19, 20, 24, and 28 are the four most important in Part Two of the novel To Kill a Mockingbird.
In chapter 19, Tom Robinson takes the witness stand and tells the truth about the events that took place on the evening of November 21st. Tom testifies that Mayella made sexual advances towards him and that he desperately fled the Ewell home when he heard Bob yell through the window. During the cross-examination, the racist prosecutor speaks down to Tom and treats him disrespectfully. Tom ends up making a costly mistake by saying that he felt sorry for Mayella. The racist jury and crowd does not like Tom's answer and he is aware of his drastic mistake.
In chapter 20, Tom's guilty verdict is read. Tom's conviction is an important moment in the novel, and this is when the children lose their childhood innocence.
In chapter 24, Scout depicts her maturity and increased perspective on life by noticing the hypocrisy of the local women at her aunt's missionary circle.
In chapter 28, Jem and Scout walk home from the Maycomb Halloween festival and are viciously attacked by Bob Ewell, who attempts to kill them. Fortunately, Boo Radley comes to their aid and intervenes in the struggle. Boo Radley ends up saving the children's lives by killing Bob Ewell, and he then carries Jem home.