"Separate students according to their academic performance(s)."
(For example, their test results.) Should I use singular or plural in this phrase?
I did some research, but the example here is quite different than mine.
Performance should be used in your original sentence. Performances would be for things such as performing in a play or something like that.
Performance, in this case, is a group noun like "clothing". It would apply to the whole of their academic performance.
In your example, the singular "performance" could be used
Separate students according to their academic performance (into different groups).
according to each student's individual academic performance
which would result in
The academic performances of the students in a given group will be similar.