Aloysium:
All of it with the exception of the parts which talk about the soul. The Catholic Church has no objection to evolution and common descent explaining the origin of the material human body. The divine origin of the human soul, and an initial pair of ensouled humans are the minimum that the Church seems to require.
The exceptions include the part about random mutations and natural selection as the primary means for the
creation of life. These two basically explain how celiac disease, cystic fibrosis, sickle cell anemia and the like remain in the gene pool and perhaps how they may have originated. These are diseases, not attributes like mathematics, or visual arts, or music, or the fields of economics, political science, philosophy, the stuff that defines human potential.
Using the term “evolution” to describe what are aspects of evolution with which the church has no issue, does not help clarify the matter. The word is used in so many different ways. What I mean by evolution is the strict biochemical meaning that is at the basis of modern thought in the various natural sciences including medicine. Probably most people think evolution in the sense of a progression upwards in complexity that is seen everywhere about us, but for which there exists no scientific explanation. Well, some secular pseudoscientific have been offered but they tend to be superficial and far worse than any proposed by the Intelligent Design people.
There is nothing inherent in the material universe that itself will result in a human being, nor an animal before that, a plant before that, going all the way back to the beginning when the laws of the universe, including time and space, were brought into existence. A common descent is spoken of in Genesis, which sees all life is made from the earth, each a separate creation moulded as it would appear today as the result of what existed in the past.
God created all life on earth, one with its environment, which we do a poor job replicating in our zoos and aquariums. It all changes - life adapts to the environment, which is transformed by its presence. Simple life forms, plants, animals, and human beings have changed since God initially brought them forth from the dust. This is what the church, as I understand it, would agree to.