Joachim Fest is German and he studied at universities in west Germany after the war, so I will try and give a little overview as to what were the requirements to attend a German university in that time.

In general the requirments of attending a university, and by extension getting a degree, were subject to a variety of changes throughout the 20th century in Germany, which shouldn't come as a surprise given it saw three different states with five different forms of government during this time. I will exlude the GDR from this, as I don't think it's very relevant to your question, as in a socialist society, attending university was something entirely different.

In Germany traditionally education has been and is a state business with little, yet constantly increasing, influence of the Reich, respectively the federal government for post 1945. When the German Reich was founded in 1871, the requirements to study at a university were manner of the states and from todays perspective are incredibly complicated. Being eligible to attend university was not the same as being eligible for a getting a degree and depending on what you whished to study the requirements would be substantially different. Covering this is beyond the scope of a post here I'm afraid and I don't think it would be particularly interesting for you either.

This was slowy but steadily harmonized and by the time Joachim Fest would attend university in post war west Germany it was more or less standardized and haven't changed all that much since, even though in general requirements have been lowered.

If you wanted to attend university you need(ed) an "Abitur" or "Allgemeine Hochschulreife" which is basically a qualified high-school diploma. Other means to attend university would be a "Fachabitur", which is a high school diploma that allows you to study in a certain field, which you already attended a specialised high school for, plus a variety of means like having finished a master craftsmenship etc.

When attending university there were three main degrees to be obtained: A "Diplom", most commonly found in science and engineering but also in other fields like certain social studies, a "Staatsexamen" which is the examination for state and board licensed professions like law or medicine and, in Fests case a "Magister". Both Diplom and Magister were largely phased out in the Bologna-reform, being replaced by bachelors and masters degrees. For sake of simplicity you can think of a "Diplom" as a Master of Science and a "Magister" as "Master of Arts", even though this comparison doesn't hold up very well for every field (some Diploms are now Master of Arts etc).

A "Magister" was different from a "diplom" not only in the fields that you got your degree in, it was also much more liberal in what kind of courses you could attend and collect "Scheine" (course assesments) for. It would be highly encouraged of students to attend a variety of different courses in order to widen their general eductaion. Magister degrees were explicitly not designed to prepare the student for a specific profession. They very much followed the Humboldtian model of higher education with a very holistic approach to formal education. You could maybe compare it with the US college education of choosing a major ("Hauptfach") and a minor ("Nebenfach"), the exact arrangements being constituted by the university.

If you read that a person like Fest studied history, arts, german studies etc it doesn't mean that Fest was considering getting a degree in all of those fields. It just means that he attended courses offered by the respective faculties some (most?) of which he could use for his admission to his Magister examination. It was absolutely normal to switch majors and especially minors during your time at university, often several times. Because you could generally submit course assesments from on major/minor for a variety of other majors/minors this wasn't seen as deviating as much as following your individual path to the education you desire.

Unfortunately I don't know exactly which fields Fest majored or minored in and when or often he changed them, but this is the general gist of how he would have organised his time at the various universities he attended.