You can do this using the search syntax LF:ChildName. LF:ChildName returns all folders that contain entries than satisfy the parameter of LF:ChildName. For your case, I would wildcard ChildName search for folders and a within folder search.

For example, to search within the folder A for student folders that have a subfolder (where the structure is Student Records\Active\A\<Student Name>\<subfolders>, you would perform the following search:

({LF:LOOKIN="Student Records\Active\A", SUBFOLDERS=0}) & {LF:ChildName="*", Type="F"}

Note that I have included SUBFOLDERS=0. I am assuming you only wish to return the student's folders, and not return the subfolders of those student folders. You can omit this if that assumption is incorrect.

Furthermore, note that I included Type=F in the ChildName part of the search, which means student folders that only contain documents and shortcuts and not any subfolders will not be returned.

Finally, if you wish to search on multiple folders at once (say, A and C), you could combine folders using | (the OR operator):

({LF:LOOKIN="Student Records\Active\A", SUBFOLDERS=0} | {LF:LOOKIN="Student Records\Active\C", SUBFOLDERS=0}) & {LF:ChildName="*", Type="F"}