Specifically, it was Professor McGonagall informing Hermione that she had failed all her exams.
Hermione did everything perfectly until she reached the trunk with the Boggart in it. After about a minute inside it, she burst out again, screaming.
‘Hermione!’ said Lupin, startled. ‘What’s the matter?’
‘P-P-Professor McGonagall!’ Hermione gasped, pointing into the trunk. ‘Sh-she said I’d failed everything!’
It took a little while to calm Hermione down.
Prisoner of Azkaban - page 234 - Bloomsbury - chapter 16, Professor Trelawney's Prediction
I should say that this occurred during final exams in year three and that it could technically be referring to just those exams or all her classes overall. Due to the context, that they were in the middle of exams, I tend to err on the side of Hermione failing just her exams. It could be construed otherwise, though, so that possibility remains open.