AP Physics C is the calculus based physics option and the one most often expected in engineering applications. It is not one exam but two: Mechanics, and Electricity and Magnetism. A student can take either or both.
Mechanics first
Electricity and Magnetism assumes Mechanics is known. Force, work and energy, rotation and oscillation all return in E&M; the path of a charged particle in a magnetic field is really a circular motion problem. So when both exams are the goal, preparation starts with Mechanics.
How much calculus it takes
Mechanics uses derivatives and integrals often, but most of it is basic: going from position to velocity, from force to work. In Electricity and Magnetism the load really grows. Integrating over a charge distribution, Gauss's and Ampère's laws, and the exponential solutions of RC and RL circuits sit at the center of the exam.
The practical rule: for Mechanics, taking calculus in the same year is enough. For E&M, integration should be secure before the exam.
The right topic order
In Mechanics: kinematics, Newton's laws, work and energy, momentum and center of mass, rotation, oscillations and orbits. Each topic builds on the one before; moving on to rotation before work and energy are secure is the most common place students get stuck.
In Electricity and Magnetism: charges, fields and Gauss's law, electric potential, conductors and capacitors, circuits, magnetic fields, electromagnetic induction.
The three most common mistakes
Writing formulas from memory. When a free response question says derive, credit goes to a solution that starts from a fundamental principle. Jumping to the final formula without writing Newton's second law or Gauss's law loses most of the credit.
Sign and direction errors. Vector components, the sign of potential energy and the direction in Lenz's law turn the right number into a wrong answer.
Neglecting the lab question. One of the free response questions is about experimental design and data analysis; linearizing a graph and extracting a quantity from its slope is a skill to be practised on its own.
Exam strategy
Each exam lasts 3 hours. The multiple choice and free response sections carry equal halves of the score. Free response awards partial credit, and every correct step shown earns marks.
So what is practised is not reaching the answer but writing the solution with its reasoning. A student who reaches the right number and shows nothing loses most of the available credit.
How long it takes
That depends on the starting point rather than on a fixed number of months. The useful measure is which of the topics above, and which parts of calculus, are already secure, and that is settled with a diagnostic rather than an estimate.