According to the book "Empress Alexandra" by Greg King, she had a degree in psychology from Heidelberg University. I've never seen this mentioned in other books. I had always thought Princesses were not permitted to go to public universities with regular people
I also have come across this anecdote, although once only (possibly via King), but I do not believe it is factual…
Often honourable and unusually gifted women were permitted to sit in on lectures at universities, but unfortunately the patriarchal system ensured that they could only ever achieve a sort of quasi tertiary education. This was achieved by measures such as prohibiting women from engaging in lectures, and even segregating them in the great halls so they were merely isolated audience members, to barring them from sitting exams and having their results published, and in most cases graduating/matriculating.
This was the case at Heidelberg University during Alexandra’s adolescence, as it was with Oxford and Cambridge; I believe one of the only possibilities may have been the University of Zürich at that time. I am not sure however how ‘honorary degrees’ may have functioned in those days, if they did at all (but that is a possibility).
Either way, if Alexandra were to have undertaken a degree, it would have taken a considerable amount of energy, determination and influence from her family, and would have been quiet controversial (I am not sure how QV would have received it), so needless to say there would be a mass of sources confirming it.