Lessing uses the word "incredulous" just once in her story. Let's look at it in context:
"He sat by the clock in the villa, when his mother was not near, and checked his time. He was incredulous and then proud to find he could hold his breath without strain for two minutes. The words 'two minutes,' authorized by the clock, brought close the adventure that was so necessary to him."
We can tell that, at first, the narrator can't even believe how long he'd held his breath. And then when he realized that his timing was correct--when he did believe his results, since the clock "authorized" them--then he was proud of what he'd accomplished. This is how we can tell from the context that "incredulous" means "unbelieving" or "not believing."
Even outside of this context, the best, simplest synonym for "incredulous" is "disbelieving," "unbelieving," "doubtful," or "skeptical."
By definition, people who are incredulous, or people who show an incredulous reaction or speak incredulously, cannot believe what they are seeing or being told. For example, if you read the first Harry Potter book, Harry is constantly incredulous when he sees magical items for the first time. He can't believe what he's seeing. And if your friend told you that she just won a billion dollars in the lottery, you'd be incredulous: you'd have an incredulous look on your face, or you'd shout "No way!" incredulously.
Here are a couple of good ways to remember the meaning of "incredulous."
First, look at how the roots ("in" + "cred") mean "not" + "believing." This "cred" is the same one you see in "credo," "credit," "credibility," "credential," "street cred," and so on. Any time you see "cred," you know it has to do with belief or trust.
Second, compare and contrast "incredulous" with the much more familiar "incredible." This will help you anchor the word "incredulous" in your mind to something that you already know. What does "incredible" literally mean, besides "amazing"? It means "unbelievable." Incredible things are so awesome or so wacky or so terrible that you can't believe them. So, while "incredible" means "unbelievable," "incredulous" means "unbelieving." Notice how "incredible" usually describes things and events, while "incredulous" usually describes people and their reactions. In other words, you talk about incredible accomplishments, incredible deeds, and incredible facts, but in contrast, you talk about incredulous speakers, incredulous stares, and incredulous silence.