“and then put out the eyes of Zedekiah.” The punishment of Zedekiah was especially severe because Zedekiah had sworn allegiance to Nebuchadnezzar in the name of God (2 Chron. 36:13; Jer. 52:10-11). It was commonly done by kings that ruled over large areas to have very severe punishments for rebellious kings; that was a major way that empire rulers kept their vassal kings from being rebellious.
“and he bound him in bronze chains.” The “he” is Nebuchadnezzar, who gave the order to bind Zedekiah.