My fear is that he will realize his presidency is irredeemable, so he'll aim to be the best at being the worst. If he deliberately seeks out notoriety/villainy for his legacy, knowing full-well that he'll never have a chance at being remembered fondly, he'll resort to crazy sh**t all in the name of being "someone" in the history books.
Is he selfish enough to nuke North Korea and accept the consequences when they retaliate...? Just maybe. We already have enough proof that he's not a good man. Kinda scary.
This is unlikely. There's no way Trump would put this much thought into it.
Hope you're right.
But given how good he is at knowing how people will respond to what he says in the immediate [not much for the long term], I'm not sure this can be ruled out.