Once you have gained the skills for deep comprehension, that you not only understand an idea, topic, or object superficially but in its complexity and can articulate that complexity to others, the next step is to understand critical analysis. Whereas deep comprehension is essentially the process of absorbing and recalling information (albeit very subtle and nuanced), critical analysis involves putting pressure on that information to test its integrity. In this stage, you begin to categorize the claims you have deeply comprehended by their truth or soundness.
To illustrate this point, let's look at an example.
Imagine that you have discovered a cave filled with treasures that appear to be from a lost civilization. Because you are equipped with the skills of deep comprehension, you begin to look carefully at each object, ensuring you absorb as much information as you can from each one. You find works of art and literature with nuanced meanings with subtexts that might be missed without your careful attention. But, at some point, an important and serious question begins to form in your mind. "Where did all of this come from?" "How do I know this is really from a lost civilization, not some elaborate and well-crafted hoax?" To answer these questions, you must engage in critical analysis. You return to each object (with which you are intimately familiar) and begin to ask different questions of each one. Instead of asking, "What does it mean" or "How does it transmit meaning?" you begin asking questions, like, "Are the claims this object makes (that it is from a lost civilization) logical?" and "Is there anything about this object that makes its arguments weak?" And so you begin. You rigorously test each object for coherence and consistency until you have uncovered enough evidence that you are convinced whether or not to believe the contents of the treasure hoard.
This is the difference between deep comprehension and critical analysis. The first aims to understand the meaning, and the second aims to evaluate that meaning's worth. To do that, we need to understand the elements or the tools to use to put pressure on claims. Then we need to identify the core of the argument, often called the premise. Finally, we must vigilantly beware of logical fallacies, accepted claims that distort an argument and make it appear to be sound when it is, in fact, not.