If you're setting a dramatic tone, "He walks forward. She clenches her fists." works perfectly fine. In fact, "He walks. Walking forward. She clenches her fist. He still approaches." might make it even more dramatic, though of course that's not a perfect example.
But there are, of course, plenty of alternatives. Lemme show you a few examples, starting with my favorite:
1: Semicolons!
"He walks forward; she clenches her fists."
I've seen you say that you don't fully understand the proper way to use semicolons, so I'll give you a brief rundown.
A semicolon separates two independent clauses, which means two complete sentences. To be a complete sentence, it needs to have a subject (the noun acting) and an action (the verb being done). A complete sentence can be anywhere from "He is." to "Despite popular belief, he is one of the brightest people in the room, and plenty of people love him."
Another important thing to remember is that the two connected sentences have to be related. If she clenches her fist because he walks forward (which was my assumption), the semicolon works. However, you shouldn't connect two unrelated clauses, i.e., "She walked; school got out for the day." There are cases where those two sentences could be connected or made to be connected, but pretend they aren't.
Unlike a comma, a semicolon doesn’t require a coordinating conjunction (FANBOYS: for, and, nor, but, or, yet, so) to connect two independent clauses. However, you can use a transitional phrase (also, however, meanwhile), but you'll need a comma after the phrase. You also don't need to capitalize the second sentence.
The point of the semicolon is that it's a longer pause than a comma, yet not as final and separating as a period; it also helps vary your punctuation. It can denote cause-and-effect and highlights the connection between two clauses. It's important to consider the intended rhythm and flow of the writing rather than using this everywhere it's grammatically correct.
2: Adding Details!
Oh, looks like Mizal already got there. Go look at that.
3: Other Subordinating Conjunctions!
"While he walks forward, she clenches her fists."
Here are some examples of subordinating conjunctions other than "as":
after, because, while, before, where, if, once, that, unless, whether, though
I'll mention that it's a subordinating conjunction due to joining a dependent clause (fragment) to an independent clause. "As he walked" is a sentence fragment on its own.
4: Coordinating Conjunctions!
"He walks forward, and she clenches her fists."
Coordinating conjunctions (FANBOYS) can connect two independent clauses and are usually accompanied by a comma. Pick one based on the meaning you want your sentence to have: contrast (“but,” “yet”), addition (“and”), choice (“or”), cause (“for,” “so”), or negation (“nor”).
When the conjunctions connect independent clauses, a comma is usually recommended before the conjunction. If the clauses are very short and closely related, the comma can sometimes be omitted: "He walked and she stared." Usually people still like commas there, but my point is you don't need them, especially if your writing is already pretty comma-heavy.
5: Participial Phrases!
"Walking forward, he notices her clenched fists."
These include a present participle (what you get when "ing" form of a verb becomes a modifier) and any other modifiers (like "forward" in this case)
They can modify nouns: "Walking forward, he notices her clenched fists."/"Noticing her clench her fists, he walks forward."/"Clenching her fists, she watches him step forward." All of these examples tell you something the subject, "he" (or "she", in the last example), is doing, beyond the action.
They can function as part of a verb phrase: "He starts walking forward while she clenches her fists." "Starts" is the verb here.
These have to be separated by commas when at the beginning of a sentence.
6: Gerund Phrases!
"Noticing his approach makes her clench her fists."
A gerund is a verb disguised as a noun (so, functionally, a noun).
Its placement in a sentence depends on the role it takes.
In "Noticing his approach makes her clench her fists," the gerund acts as the subject, and so goes at the beginning.
"She began clenching her fists in frustration." The gerund phrase is the object of "began", so goes after that.
"He times his steps with the clenching of her fists." That was hard to think of an example for. Anyway, modifying the preposition makes it go at the end of the phrase. See what I did there?
7: Prepositional Phrases!
"With each step he takes, her fists clench."
A prepositional phrase starts with a preposition and includes its object along with any modifiers.
Examples of prepositions: above, at, below, beside, between, in, near, on, under, after, before, by, during, since, until, across, around, past, through, to, toward
There are more, but I'm sure that's plenty.
Hopefully all that helps a little.
Links to click for similar (better) information:
Basic Sentence Structure: Additive Sentences
Cumulative Sentences, Part 1
Cumulative Sentences, Part 2
Relative Sentences