Sorry Schizm.
Try the following books:
Babylon - Joan Oates ISBN 0-500-27384-7 (particularly chapter 5 pages 126 - 139) Assyrians, Babylonians, Persians and Greeks.
The Cambridge Ancient History Vol III Part 2. The Assyrian and Babylonian Empires and other States of the Near East, From the Eighth to the Sixth Century B.C. - various ISBN 0-521-22717-8
This volume is written by various authors, some of whom are often quoted by the Watchtower Society. Chapters to read on this subject are: Chapter 21: The Fall of Assyria (635-609 BC) by Joan Oates; Chapter 27: Babylonia 605-539 BC by D.J.Wiseman; Chapter 30: Judah until the fall of Jerusalem 700-586 BC by T.C.Mitchell; Chapter 35: Egypt, The 25th and 26th Dynasties by T.G.H. James.
For brief information about the rise of the Persian Empire see 'The Greek and Persian Wars 499 - 386 BC by Philip de Souza ISBN 1-84176-358-6 pages 19-24 Kyros the Great and the Persian Empire.
For a full list of Egyptian rulers and dynasties try 'Egypt, The World of the Pharoahs' edited by Schulz and Seidel ISBN 3-89508-913-3 pages 528-529 for chronological table based on Jurgen von Beckerath (Chronologie des pharaonischen Agypten)
Hope these references are helpful.