The groups are
BELGIEN, FRANKREICH, RUSSLAND, PORTUGAL: the German names of four European countries
ERSATZ, OVERSAW, REVRESAL, VERSATILE: four things with ERSA as substring
CRITIC, GRAM, LOGIC, PER: four things that can come after DIA to make words
CANE, DATE, DINE, TA: four things that can come after IO to make words
with the proviso that
IOCANE isn't really a word outside The Princess Bride. (I know, it's inconceivable.)
And now the final answer is
the German word for Europe
like DIA, ERSA and IO, the name of a moon of Jupiter (and, not coincidentally, like them a Greek mythological figure associated with Zeus).
is presumably because TITAN is also a moon (albeit of Saturn rather than Jupiter) and the title of a number of beings in Greek mythology.
Since this was kinda supposed to be educational, here are a few notes on the solution process for newish solvers, and some comments for the author.
The first thing that jumps out at me is that BELGIEN, FRANKREICH and RUSSLAND are all German country names. PORTUGAL might be but of course it's also the English name. ERSATZ isn't a country name but is also a German word. So, first question: is PORTUGAL also the German name for that country? It turns out that it is. This gives us a pretty plausible group of four. Of course the puzzle creator could be playing with us and trying to mislead, but this is explicitly billed as a relatively straightforward puzzle so probably not.
looking over the remaining words, I notice two things. One is that a lot of them are rather short. PER and TA are especially suspicious. It seems likely that these are prefixes or suffixes of something somehow. What about the longer ones? In descending order of length we have VERSATILE, REVERSAL (hmm, those are interestingly similar-sounding), OVERSAW (wait, do they all have VERSA in?) and ERSATZ (hmm, not all VERSA or even VERS -- but all have ERSA). That seems likely to be another group of four, especially as the ones it leaves are all nice short words likely to be prefixes or suffixes. It's not clear how "they all contain ERSA" is going to end up having anything in common with "German country names", but no matter; perhaps everything will become clear later.
At this point
we have CANE, CRITIC, DATE, DINE, GRAM, LOGIC, PER, TA, and I am strongly suspecting that they will turn out to be prefixes or suffixes of a couple of things. DATE and DINE sure look like suffixes, for instance. I spent a while trying to think what might go in front of some of these and I confess I didn't find anything convincing, so I turned to computerized help. The excellent tool Qat can answer questions like "find me something that's a prefix of both DINE and DATE" (you put in "Adine;Adate") but I felt that was a bit too cheaty, so what I actually did was to look for words ending in individual words from the list and scan them by eye looking for promising prefixes. When I was looking for "*gram" and saw DIAGRAM, it hit me that DIAPER was also a word -- ah, and DIACRITIC and DIALOGIC, not that the latter is at all common.
we have three of the four groups, and if we haven't made some unfortunate guesses the last group is CANE, DATE, DINE, TA. If you are fortunate enough not to consider CANE first, it's not hard to spot IO- even without electronic help.
At this point we have
German names of European countries; -ERSA-; DIA-; IO-. Well, the German for Europe is EUROPA and that and IO are both moons of, errrm, I think Jupiter. (Check? Yup.) But what the hell are ERSA and DIA? Find their Wikipedia disambiguation pages ... and, lo, it turns out that both of these are also moons of Jupiter. So EUROPA is connected to them all and we're done.
So, was there a reason beyond bad luck why this didn't get solved by a less-experienced solver in the first day? Where were the difficult points?
I personally found that even when I was sure I wanted prefixes for the short words, my brain was not good at finding them. Maybe that's just me, but I'm guessing it's just genuinely a bit tricky. I think CANE was a bit of a low blow, since IOCANE is not really a word and (alas) not everyone has seen The Princess Bride. And, for the final step, maybe I'm just ignorant but I had never heard of ERSA and DIA either as mythological figures or as Jovian moons. I guess they're relatively obscure.