What are the main areas of study in astroparticle physics in relation to astrophysics?
Dark matter, dark energy, nuclear astrophysics, high-energy and low-energy neutrino astrophysics.
Astrophysics is the science which aims to "ascertain the nature of the heavenly bodies, rather than their positions or motions in space."
Astrophysics studies all extra-terrestrial bodies, such as other planets, supernova's, stars and blackholes, as well as the cosmc microwave background, the interstellar medium, dark energy and dark matter. It does by examing the emissions of the latter across the entire electromagnetic spectrum, and then uses the results to determine properties such as luminosity, density, temperature, chemical composition and more. To study astrophysics one typically needs a broad range of skills in physics and chemistry, including quantum mechanics, particle physics and molecular physics.
The study of astroparticle physics, or particle astrophysics, "is a branch of particle physics that studies elementary particles of astronomical origin and their relation to astrophysics and cosmology"
Astroparticle physics thus covers quite a lot of what astrophysics does, which includes dark matter, dark energy, nuclear astrophysics, high-energy and low-energy neutrino astrophysics. However, astroparticle physics also deals with particle cosmology, high-energy, VHE and UHE gamma-ray astronomy, and high-energy cosmic-ray physics.
I hope that helped!