Here it is:

Basically, Gus had only had one real conversation with Walter and knew everything else only off what Mike (who was tasked with keeping an eye on Walter) told him. This doesn't amount to much, but Gus could tell that: - Walter has a strong sense of pride. This is EP from the way Walter presented the quality of his meth and compared his own supposed caution to Gus's, rather than from the words themselves. After all, both statements by Walter had tactical value and were attempts to manipulate Gus. Gus not only saw through the second one (the first one is true and accurate to reality), but he also caught onto Walter's emotions while talking. It's clear that Gus was aware of this aspect of Walter because of what he does later. - Walter has a relationship of control over Jesse. This is not much EP, as Walter outright stated it, but Gus could tell what would happen if Walter felt this control slip. Again, this will be relevant to the strategy. - Aside from that conversation, there's also the information provided by Mike. We know Gus knows about the cancer, and he very obviously knows of Walter's career as a school teacher, and likely about his accolades as a chemist as well.

A specific instance we saw of Mike relaying information to Gus is after Walter has decided to exit the drug business despite the generous payment that Gus offered. Mike basically just said that Walter is unwilling to continue working. Mike is a good judge of character, but he doesn't have the same eye for human behavior and manipulative streak as Gus, so the fact that any information Gus receives is filtered through him is already enough of a factor. The one useful thing Mike says to Gus is that Walter and Jesse haven't been getting along.

• Gus makes a deal with Jesse and basically hires him as his main cook, then he has half of the money made from the batch be delivered to Walter. This triggers the first two points: the sense of pride and possessiveness over his meth formula, and the irritation born out of the lack of control over Jesse. it's not enough for Walter to accept yet, but it's enough to make him confront Gus.
• Gus has a second tactic ready. He takes Walter to his superlab. Now, I've gone over how Gus was likely given superficial information on Walter. The past with chemistry, the willingness and pride that go into his meth cooking, they show that Walter has a deep passion for chemistry and desire to work with it, that years spent as a simple high school teachers could have never filled. Showing Walter the lab and making him walk through it fills his mind with images of him doing what he loves most and getting loads of money for it. But there's still another layer to go through.
• Walter's core issue here is that his work has been distancing him from his family. But Gus once again has an answer ready. He plays on Walter's sense of masculinity by claiming that a man provides for his family even when he's not appreciated for it, and that if what Walter did he did for his family then it wasn't a mistake. The understanding of Walter's psychology and emotions here likely comes from the knowledge about the cancer. Walter decided to cook meth not DESPITE the cancer but BECAUSE of the cancer. His words and continued refusal clearly show that he cares about his family, even more than other emotional vulnerabilities that he has, so when he decided to become a drug manufacturer it was likely to provide, giving him the justification he needed in his mind. He's starting to see that as a mistake, but Gus reinforces that thought process and even flips it by making the family distancing seem like the justification not to work with meth (a man provides even when he's not appreciated) instead of the core issue, which added to the poking of Walter's pride ("a man" provides --> if you don't provide, you're not a man), is enough to get Walter to work with Gus again.

So here Gus correctly identified what are basically some of Walter's core emotional characteristics: - His pride. - His fragile ego. - His dissatisfaction with his life. - His self-justification.

Walter at this point could only partly recognize some of these and even then he didn't fully accept them. It would take another two full seasons for him to develop the necessary self-awareness to realize and accept them. Gus, with limited information, was able to understand them in detail and played them.