I must confess that I'm not certain that I understand your question completely, but I will try to answer them.
> Batch application starts ->Communicate to Web Service ->Communicate to Servlet -> Final Result goes to User Interface Application
Out of the box (no configuration required), I would expect that AppDynamics would discover this transaction at the Web Service, and provide visibility like this:
Web Service ->Communicate to Servlet -> Final Result goes to User Interface Application
If you add a POJO Transaction Detection rule in the Java method that begins the Batch processes, you should see the entire execution path:
Batch application starts ->Communicate to Web Service ->Communicate to Servlet -> Final Result goes to User Interface Application
In your screenshot, if you right click the highlighted method and select "Expand All", the Call Graph will expand to expose the "exact class and method responsible for [the] asynchrous call". You should be able to drill down from the "Async Activity" pop up dialog to the downstream thread.
Regards,
Brian Wheeldon