If an employee is set as a batch tutor and teaches at least one subject, then that user can mark the attendance for the batch (attendance type should be daily). There is no need of giving any extra privileges for that user to mark the attendance. More over the same employee can be assigned as tutor for more than one batches so that he gets the same privilege over the other batch too.
Normally a batch has one group tutor. You may however add more than one tutor in case your institution has a practice of having more than one tutor for a batch.