In simple terms, the main changes made after Port Arthur involved making the laws across Australia reasonably consistent (most firearms law in Australia is state law not Commonwealth (Federal) law but an agreement was signed between the state to try and ensure a greater consistency.
Universal licencing and registration became the law across the country (it was already law in most states before this), and you now had to have different types of licences for different types of guns, rather than a simple firearms licence (again, some states had already required this). In particular, a large number of semi-automatic weapons that had been able to obtain on a normal licence, now required a higher level licence which was harder to get.
Basically the most common gun licence in Australia (which is quite easy to get as long as you don't have a criminal record) is what is called a Category A/B licence. That allows you to own non semi-automatic long arms. Basic semi-automatics require a Category C licence and that's harder to get - not impossible, but it takes some work to do it and you have to provide a specific reason you need a C licence rather than just an A/B licence. Handguns also require a special licence - Category H. Again, you can get one but again you have to provide a specific reason you need a H licence and 'self defence' is not accepted as a valid reason by itself.
More powerful semi-automatics or automatic weapons are Category D or E, and most people will find it extremely difficult to get a D licence, and virtually impossible to get an E.
All weapons must be registered. All must be securely stored when not in active use. And you need to make a specific application to purchase any new weapon. The application is likely to be granted if you are licenced for the weapon, but it delays things and makes it far more complicated than it needs to be.
This is quite interesting. One thing I have found alarming is that this “ordinary person” had so many guns.
Without really knowing I imagine Australia is simpler to manage than the US - people I know who have gone there and managed to have business there, have said it was like the US in the 50s or 60s.
Perhaps we should look at what has worked regarding massacres in Australia.