The brother of a woman attacked by a shark at a popular Sydney beach has shared an update on her progress since the incident.

Leah Stewart, 34, was swimming during the day, between the flags at Coogee beach when she was attacked on June 13.

The mother and teacher suffered serious injuries to her arms and legs, significant blood loss and fractures throughout her body during the attack.

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Due to the severity of Stewart’s injuries, doctors later amputated one of her arms, while wounds contaminated with sand and debris caused an extreme risk of infection.

However, Stewart has continued to fight, with doctors bringing her out of an induced coma as her condition continues to improve.

On Sunday, Stewart’s brother Joshua shared an update on her condition, revealing she has had trouble sleeping but is grateful for support received from well-wishers across Australia and beyond.

“Leah has had some challenging days but has found real strength from your kindness and support, and wanted to pass on a huge thank you to everyone who has shared her story, sent her uplifting messages and supported her,” Joshua said in an update on fundraising site GoFundMe.

Coogee shark attack victim Leah Stewart has had trouble sleeping since the incident. Credit: AAP

Stewart has spent weeks in hospital recovering from the shark attack on June 13. Credit: 7NEWS

“Since the incident Leah has had difficulty sleeping, and on those nights she’s been reading back through your messages, not only from her family and community in Australia and her whanau in New Zealand, but also from people all across the world. They’ve given her real comfort and strength.”

The fundraiser has received over $540,000 in donations, with Joshua saying the family looks forward to “replying to all the really beautiful messages we’ve received”.

Thousand of swimmers united at Coogee for a swim-out to support Stewart and her family. Credit: 7NEWS

“Leah is beyond overwhelmed at the amazing support she has received and that her story has resonated with so many people. Thank you,” they said.

The shark attack at such a popular swimming beach rocked the local community, prompting a swim-out led by Coogee Surf Life Saving Club and Randwick City Council attended by over 1000 people, with thousands more gathering to show their support.