What is the process for applying for a retirement visa in Thailand as an Australian citizen?

You really need to read the requirements on the Thai visa website

You can enter on visa exempt for 60 days but if you want to retire in Thailand and are over 50

Apply for non O visa from home, ensure 800 K THB in Thai bank account for minimum 2 months and then apply for 12 month extension based on retirement at immigration office

I have no idea how you do it once in country but again if you read the website it will be outlined for you

Get a NON O before you leave Oz. That is the easiest way to do it. Then use your funds, that you already have in your Thai bank, to get a year extension of stay. If not, do as Tod says. ;)

You got your wires crossed a bit

As an Aussie wouldn't get any "entry visa"

People from 90+ countries (Australia included) get stamped in FREE for 60 days on the "visa exempt" entry program (which has been 60 days since July 15th 2024)

Once you're here you'd go to your immigration office, get the hand out listing the documents needed to apply for the in country 90 day Non-O visa based on retirement for 2000baht.

You need a minimum of 15 days left on your entry stamp to apply for that visa at most offices. When you apply you will get a receipt that says to come back to the office in 2 weeks. When that time runs out, you return to the immigration office and they ink in the Non-O visa, and a new 90 day stamp.

Then you wait until you have 30 days or less left on that stamp, go back to the immigration office with all new documentation and apply for a yearly "extension of stay" based on retirement for 1900baht. That gets issued on the spot