I am doing BSc (Adv.) at the moment, and you don't have to do any advanced units in the first year, at least 12 cp (2 subjects) in the 2nd year and at least 24 cp (4 subjects) from one discipline in the third year. As well as that you have to maintain credit average (65%) in 2nd and 3rd year or will get kicked out to "normal" BSc.
As for pre-requisite for individual advanced units, I can only answer for mathematics, chemistry, biology and Physics.
In Math, to do advanced subjects you need to have done Math Extention 2 or have got 90%+ from Extension I. There's higher requirement for SSP Units: on top of my head, I think it was 90% in Extension 2 and UAI of around 98.7+.
For Chemistry, you need to have Band 5 or 6 from HSC Chemistry, and again think you need Band 6 and UAI of 96.4+ for SSP.
Physics Advanced Units would require Band 6 in HSC Physics. No idea for SSP Units-I haven't done Physics at all this year.
As for Biology Advanced subjects you would probably need Band 6 in HSC Biology.
However if you get into normal science units in the first semester and get distinction, you usually can get into an advanced unit in the second semester.
Hope that helps.