Is the use of semi-colon correct here?

Solution 1:

A comma belongs here. A semi-colon links two independent clauses that are closely related in thought, which is not what you have here.

Your thought that "...because the first clause doesn't seem to be an independent one since it doesn't convey a complete idea" is the exact reason why you need a comma instead of a semi-colon, because it's a dependent clause.

Solution 2:

Though the usage has been criticized, not only ... [but] also functions as a coordinating conjunction even without the contrasting but, thus not requiring a semicolon to join two independent clauses. Since there appears to be a question whether this is indeed the case, look at the clauses without the conjunction:

Walker was a trailblazer in the medical field.

She was a visionary who bravely challenged many of the social prejudices of her day.

Both clauses have the structure Subj. + copula + predicate noun — clearly independent clauses.

The lack of the contrasting but does, however, suggest a colon might even add more drama to this sentence, as others have suggested. Whichever you decide, a semicolon would be the wrong punctuation here.