也 and 还 diference not clear enough
还 can be translated to something like "not only that" or "furthermore" in English. On the other hand, 也 means something like "and" or "also". Their literal meaning is almost exactly the same, but 还 places an additional emphasis on the object that comes afterwards.

In your example


  他上课时开始不专心听讲。他的学习成绩也越来越差。


This roughly translates to


  He doesn't listen attentively during lessons. His results are also getting worse over time.


This places more or less equal emphasis on “不专心听讲” and “学习成绩”. On the other hand, the following version


  他上课时开始不专心听讲。他的学习成绩还越来越差。


roughly means


  He doesn't listen attentively during lessons. Not only that, his results are getting worse over time!


So there is a greater emphasis on the 学习成绩越来越差 in the latter version with the 还 over the 也, and there's a slight difference in meaning. So although both are perfectly grammatical sentences, they do have slightly different meaning, and it depends on which meaning you want to express when choosing terms.