I don't necessarily think that Achebe tries to deliberately paint Christianity in a negative light. I rather think that what he tries to do is to honestly present an accurate description of how Christianity entered many traditional cultures, and the kind of mistakes that were made and the way that indigenous cultures suffered as a result.
Keep in mind that Christianity is not the only religion depicted in Things Fall Apart. Achebe focuses on Ibo religious practices, too. Does Achebe draw any parallels between Christian and Ibo practices? This would indicate that he is expressing views on religion in general. Does he completely separate Ibo and Christian religious practices? If so, does he seem to "prefer" one? Does he deal with religion by itself, or with the people who participate in it? Does he depict different "kinds" of religious people?
Achebe was raised by Christian parents, so there was a definite respect for this religion in his writing; however, his portrayal of their entrance into Ibo society is brutally honest and often portrays Christains in a negative light. Of course, we may also view much of the Ibo's behavior negatively as well. Achebe left the judgment up to the reader. It appears that his ultimate goal was to show how lack of understanding and cultural as well as religious differences can lead people to take drastic measures in order to protect their lives and beliefs.
I believe that his perspective on Christianity was a negative one. Though many characters of his story have Christian first names, denoting that someone is both Christian and African, this conflict seems to bear in favor of traditional African thinking and it seems that Western influences hinder progress rather than assist it.