Yes, both are correct. 'Difficulty' can be both an uncountable and countable noun.

Although both sentences would be correct, they have slight different meanings. "She has DIFFICULTY with her studies" only tells you that it's DIFFICULT for the person to study (or to have good marks, whatever). But when you say "She has DIFFICULTIES with her studies", you're stating that she has MORE than one difficulty regarding her studies, that is, she faces multiples obstacles when it comes to studying. That's how I interpret those two sentences, at least. They have similar meanings, but there's a slight nuance between the two.