How to claim in Australia?

I would like advice on creating a claim against an app development firm we hired, as they are in breach of contract. We used Upwork, but they were unhelpful in mediation. The company doubled the price halfway through the project after we had committed. We have detailed screenshots and proof to hold them accountable. Our mistake was making a contract but agreeing to hourly charges. What can we do from here? We live in Australia.