If you want to be a theoretical physicist you have to do a lot of maths. Infact, the people who started doing Physics at Cambridge but who want to go into a PhD in theoretical physics end up swapping into maths for the 4th year.
Almost all the theories popular science books are written on are just maths with a vague context. There's plenty of 'advanced physics' which can be done without doing huge quantities of maths, solid state physics or condensed matter, but if you plan to be a string theoriest or do research into supersymmetry or black holes, you'll need to do a LOT of maths.
The list 't Hooft gives in that link seems to be more the route a physics student who bends their study towards maths would cover. I've not done courses in electronics or optics as such and only touched on solid state physics or 'atoms and molecules', they are not sufficently mathsy to be done by the maths department (that's not to say they're bereft of maths).
The amount of material in each of those items in 't Hooft's list is probably 1~5 times a whole A Level and you'd cover that in a term, maybe two (along side other courses). Sounds scary, but think about how much time you spend in lessons doing example after example after example, a teacher might spend 10 minutes explaining a new method and the next lesson and a half you'd do examples. None of that in uni, it's "Here's a result. And another. And another" with the occasional single example thrown in.