ASOIAF: When, if ever, did Tyrion figure out that Jaime and Cersei attempted to murder Bran

He pretty much intuitively figured it out in Game of Thrones while having breakfast with Jaime and Cersei in Winterfell not long after it happened.

AS is typical in any Lannister POV there is always much more going on in the subtext, between the lines, than what it is. No, nobody up and tells him. But he knows. And Jaime knows he knows.

If that's not enough there is this passage from A Clash of Kings, Chapter 54, after the news of Bran and Rickon's 'deaths' reaches King's Landing:

"I trust you're pleased," he said as she read. "You wanted the Stark boy dead, I believe."

Cersei made a sour face. "It was Jaime who threw him from that window, not me. For love, he said, as if that would please me....when did our sweet brother ever stop to think?

Now, as to the other attempted murder, i.e., the  attempt with the knife that Catelyn and Summer thwart at the beginning of Game of Thrones, Tyrion truly does not know about it when Catelyn arrests him--he doesn't even know that it happened at all.

Later, in the books, in A Storm of Swords, he eventually decides that it's Joffrey who is guilty and very subtly insinuates it to Joffrey; who seems to react as if he knows exactly what Tyrion is implying. And Jaime, later, also figures that it was Joffrey that sent the assassin.

This central mystery is pretty much cleared up by book readers,though there are some people who think that the evidence is relatively thin. However, due to the fact that both Tyrion and Jaime blame Joffrey and afterwards GRRM seems to drop the issue, I assume that that's as close to a solved mystery as we're going to get.

The show is a different story. The show obviously just dropped this mystery. It's unclear if the blame will ever fall on Joffrey as it does in the books.

The show is like that. The thing is, the show gained in popularity after the first season; and a lot of people like it who missed the first season. Some of those people won't remember the knife and that mystery of the first season; others just watch the show for the tits and blood--the showmakers try to accommadate these people as they are the reason for the show's vast popularity...So the careful watcher is, sadly, left with these unresolved issues.

Written December 27th, 2015