I’d say algebra is probably the toughest in its own right: lots and lots and lots of definitions and many students dislike that. Things like analysis, linear algebra, topology: they’re a bit more intuitive, at least to me and several students I know.
I think the most advanced branch of mathematics is Calculus and Number Theory. These are the two branches widely used in any field. For example Structural Engineering, Software Engineering, Robotics, Electronics, etc.