Welcome to ELL.SE! Let me be honest with you, I'm not fond of any of your examples. My problem is that "clearer" is modifying "it," but what is "it" that it becomes more transparent (the object, whatever "it" represents) as something unexpressed happens? What is it that was becomming more clear?
I saw it become clearer and clearer.
Let's start with your first example. You don't tell us what is happening when this sentence takes place, nor do you tell us what "it" is. "It" must be something that can be seen (visually) and that can become transparent or "not occluded."
As the wind blew through the valley I saw the sky become clearer and clearer.
My example, above, replaces "it" with "the sky" and the unexpressed action is expressed as the wind blowing through the valley. This makes sense.
As the person approached me in the darkness I saw him become clearer and clearer.
This example is incorrect — specifically, it's grammatically correct but lexically incorrect. By this I mean the sentence structure follows the rules of construction, but the wrong words are used to describe what's happening. The sentence describes the "person" becoming more transparent (think "invisible man") as he approaches. This idea would be correctly expressed this way:
As the person approached me in the darkness my vision grew clearer and clearer.
In this example, it isn't the person who's becoming clear, but my vision. This makes sense as people are visually more obscured by distance in the dark.
I saw it becoming clearer and clearer.
This example of yours is grammatically correct so long as its context is appropriate. Again, what is "it?"
I saw the pond becoming clearer and clearer.
I saw the sky becoming clearer and clearer.
"It" must refer to something that can become transparent. Water and the sky can, an idea might (it very much would depend on what you said earlier), solid, opaque objects (like people) can't.
This statement also assumes an unexpressed action. Unexpressed actions can be said in earlier sentences, but as an example now:
As the sediment settled, I saw the pond becoming clearer and clearer.
And for your last example:
I saw it was becoming clearer and clearer.
A more advanced user of English may disagree with me concerning this example (and if so, I welcome their comments), but I believe this example is grammatically incorrect.
"Was becoming" is the past simple continuous form of the verb. But "saw" is the simple past form. Your subject needs to be "continuous" or describe an action that was finished during the "continuous" action. Thus:
The sky was becoming clearer and clearer while the wind blew.
I closed my umbrella while the sky was becoming clearer and clearer.
In both examples, the word "while" associates one action with the past simple continuous action. There are other words you can use to do this (such as "as"), but this example should suffice. "Continuous" sentences are complex and deserving of your study.