The 29-year-old was helped by residents in the area – including a local vet who had just purchased a set of bandages, which she used to create a tourniquet to stem the bleeding.
Surgeons worked through the night to save Ms O’Neill’s leg from amputation, according to Sydney’s Daily Telegraph.
She is expected to make a full recovery.
In a statement, released through the hospital where she is being treated, Ms O’Neill thanked her “heroic and very kind neighbours for the critical assistance they provided her”.
She added that her likely recovery was a “testament to their extraordinary skills”.
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Woman injured in Sydney shark attack
Police in New South Wales said Ms O’Neill suffered a “serious injury” to her right leg during the attack, which is believed to have been carried out by a bull shark.
The incident happened about 20 metres from a jetty in Elizabeth Bay, an upmarket inner-city suburb near the iconic Sydney Opera House and the city’s central business district.
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Shark sightings along Sydney’s ocean-facing beaches are common, and the harbour is known to be an important habitat for bull sharks and their young.
However, shark scientist Amy Smoothey said attacks in the area were “really rare”.
“The last incident that occurred in Sydney Harbour was in 2009,” she told the Australian Broadcasting Corp.
Known for their aggressive, territorial nature, bull sharks are large and usually found in warm, shallow waters, but can survive in fresh waters and are known to swim up rivers.
Bull sharks, great whites, and tiger sharks are responsible for most recorded unprovoked attacks on humans.
In 2009, an Australian navy clearance diver was mauled by a bull shark during a training exercise in the harbour. The shark tore off his arm and part of his leg.