With the photo you provided it is difficult to identify the insect damaging your fruit tree. The first step in getting rid of garden pests is identification. I suggest you take a sample of the bug to a local gardening store for proper id and treatment options.
I understand you don't want to use chemicals. Therefore, praying mantis, ladybugs, and green lacewings are outstanding alternative to chemical sprays. In addition, encouraging toads, birds and lizards to take up resides in you garden is a good step to prevent future garden pest problems.
I hope this helps. Steve @ different-kinds-of-plants
