How was Isaiah's prophecy accomplished against Israel and Judah?

Answer 1

Your question may be confusing accomplished and fulfilled. Isaiah's prophecies were accomplished through visions which he merited to receive from God.

Those of his prophecies which were directed against Israel and Judah were fulfilled when Israel was exiled by the Assyrians, and Judah was exiled by the Babylonians.

See also:

How many Isaiahs?

Israelite prophets

A few fulfilled prophecies:

• The destruction of Babylon (Isaiah 13:19).
• The fact that billions of people have come under the influence of the Abrahamic belief, with the Greek, Norse and Roman gods now long-defunct. This is an (as yet) partial fulfillment of Isaiah 2:18.
• The prophecy that the Torah would never die out (Isaiah 59:21) has been fulfilled, against all odds.
  
• The prophecy that the recently-barren Israel would once again bloom (Isaiah 41:18-20), has been fulfilled.

Answer 2

Isaiah 1:1 introduces the book as the work of Isaiah, son of Amoz, who lived in Judah during the reigns of the Judahite kings Uzziah, Jotham, Ahaz and Hezekiah, early in the seventh century BCE. The Book of Isaiah then omits the 150 year period from Hezekiah to the fall of Jerusalem and recommences with the Babylonian Exile. The remainder of the Book of Isaiah was written in Babylon in the middle of the sixth century BCE and finally after the Return from Exile. The three authors of the separate works that later became the Book of Isaiah are sometimes known as First Isaiah (I Isaiah), Second Isaiah (II Isaiah) and Third Isaiah (III Isaiah).

Much of First Isaiah's writing was in the form of oracles, vague comments and predictions that could be interpreted in many ways. Reading them in hindsight, it is almost always possible to link an oracle to a future event in some way. First Isaiah witnessed the fall of Israel, so at the time he wrote his book, this was no longer a prophecy. He did not predict the Babylonian Exile, which was far off in the future, but Second Isaiah wrote of the events in Babylon.