Perylene tetracarboxylic acid bisimides are compounds that show intense visible light absorption and exhibit excellent chemical, photochemical and thermal stability. As such, they have been widely used as dyes and have a range of industrial applications. These dyes have also been investigated for various applications in aqueous media as chromonic liquid crystals: lyotropic systems characterised by the association of aromatic mesogenic cores into stacked structures. In this study, we focus on one perylene dye bis-(N,N-diethylaminoethyl) perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride, PER, and study its self-assembly in aqueous solution through both atomistic and coarse-grained molecular models. All-atom molecular dynamics simulations demonstrate spontaneous self-assembly into chromonic H-aggregate stacks with an interparticle twist between molecules. The coarse-graining of complex chromonic mesogens introduces a wealth of subtle complexities that presents a significant challenge to overcome. Consequently, we developed coarse-grained (CG) models using both bottom-up and top-down approaches: the multiscale coarse-graining method (MS-CG) in the form of hybrid force matching (FM) and the MARTINI 3 force field, respectively. We discuss the successes/deficiencies of these approaches and introduce changes to improve upon their performance and representability. For the MARTINI 3 model, careful optimisation of parameters allows it to exactly reproduce the atomistic self-assembly behaviour including the relevant thermodynamic properties in solution. The bottom-up CG model, produced using a conventional MS-CG treatment, fails to reproduce most of the target properties, but the implementation of the potentials into a combined FM-MARTINI 3 framework allows the recovery of the correct self-assembly behaviour in solution.