I think learning basic atomic theory, whether that is through a chemistry text or a physics text, is quite necessary. Understanding how electrons work and how they fit in different energy levels and how this all relates to bonding is very important to understand hard-core quantum mechanics. I don't know how advanced of physics you are going to go on to, but if it's really, really advanced physics, learning the basics of crystal formation, molecular orbital theory, and solid-state structures also would be good to have. And you should familiarize yourself with radioactivity (e.g., difference between alpha and beta decay) and relativity.
Most suggestions already given were topics in a standard two-semester intro course in physics, where the first semester is Newtonian mechanics and basic thermodynamics and the second semester is electricity, magnetism, and optics. But since you said "advanced physics," that signals to me that you should be brushing up on the basics of modern physics, too. And I'd assume that you are quite gifted in math to be pursuing advanced physics, but even if you haven't had all of the math you need to do quantum mechanics, you don't need the math to learn the concepts. I have NVLD and have always struggled in math, but that doesn't mean that I don't know the conceptual material in advanced atomic physics/chemistry. As an example I use frequently, I may not be able to understand the Schrodinger equation itself, but that doesn't mean that I don't understand what the Schrodinger equation signifies and tells us.
And when it comes to physics, my best knowledge comes from atomic theory, and this is because I have had to take a lot of chemistry for my neuro degree. (And that's the area of physics, besides electromagnetism, that is the most important when it comes to neuroscience.) So, I can help you with texts in that area, if need be.
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Helinger: Now, what do you see, John?
Nash: Recognition...
Helinger: Well, try seeing accomplishment!
Nash: Is there a difference?