Catherine Rossiter filed an application in the Federal Court on Thursday for information on the bank's risk management systems due to a lack of clarity on the disclosures in ANZ's 2022 annual report.
"I'm worried that ANZ is not playing the part a financial institution should be playing in the 21st century," Ms Rossiter said.
"I think it's important for shareholders and the community at large to understand if a major bank is taking these risks seriously."
Though ANZ's annual report labelled climate change and biodiversity loss as "emerging risks", it is not clear whether those risks were dealt with through the bank's risk management framework, Ms Rossiter says.
The document mentions "biodiversity and natural capital loss are addressed in various ways by ANZ's risk policies and processes", stating its business customers are expected to adhere to industry standards when managing environment impacts.
The bank has worked with its 100 largest emitting clients on "encouraging and supporting them to identify and manage their potential impacts", according to its 2022 report.
Jess Holgersson, Ms Rossiter's legal representative and senior associate at Equity Generation Lawyers, the case is a world first.
"It is certainly the first time a shareholder has sought access to the Risk Management Framework of a financial institution regarding the twin risks of climate change and biodiversity loss," she said.
"These systems and frameworks are key to the operations of the bank, and responsibility goes all the way to the board."
The court application comes as Westpac announced on Monday that it would set a zero-deforestation target for loans to beef, dairy and sheep farming and further tighten lending to new coal, oil and gas projects.
Meanwhile, National Australia Bank told its high-emitting customers on Thursday to prepare climate transition plans by October 2025.
"ANZ's peers are significantly reducing their fossil fuel lending," Ms Rossiter said.
"ANZ appears to be a climate and biodiversity laggard, and I want more information on how the bank is governed."
On climate change and biodiversity issues, ANZ is considered the worst performer of the Big Four banks.
According to activist group Market Forces, ANZ loaned $2.6 billion to fossil fuel clients in 2022, roughly 35 per cent more than Westpac and NAB, and 10 times more than Commonwealth Bank.
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