Help me parse this sentence, please?

The sentence is structured like this:

Subject clause: a withdrawal of belief in psychoanalysis

Verb: is

Predicate phrase: observable as a tendency of our culture ("observable" is an adjective modifying the subject, and the rest of the phrase modifies "observable")

"We no longer feel that it can solve our emotional problems" is a second, complete clause that can stand alone as a separate sentence. The whole sentence could be written as such:

A withdrawal of belief in psychoanalysis is observable as a tendency of our culture. We no longer feel that it can solve our emotional problems.

The sentence uses "non-standard" word order, IMHO in a misplaced attempt to seem more academic and authoritative. The natural order would be...

A withdrawal of belief in psychoanalysis is observable as a tendency of our culture.

...wherein is is the Verb, preceded by Subject, followed by Predicate. The part after the semicolon can effectively be treated as another sentence, as @spotlightdev notes.