The woman who was attacked by a shark at Sydney’s Coogee Beach has been identified.

Leah Stewart, 35, was swimming with two friends within the flagged area when she was attacked on Saturday morning.

She suffered critical injuries, and is still fighting for life in hospital.

Locals told 7NEWS.com.au the young mother was swimming about 30m offshore near the centre of the beach when she was attacked.

A witness said there was a large amount of blood in the water following the attack.

Surf lifesaver Charlie Verco, 24, raced towards danger to help save Stewart as the shark continued circling in the bloody water.

“I’d like to think I did enough to get her in fast enough,” he told 7NEWS.

“Once I had her next to me, I was just going, ‘keep your head above water, keep breathing, you’re doing really well, we’re almost at the beach.’

“Just anything, I guess, to feel the silence. It wasn’t conversational. She was not in a great way.”

Footage showed Stewart clinging to life on the hero’s paddle board while a shark alarm blares in the background as he brought her back to shore.

On the beach was an off-duty critical care doctor, paramedics and lifeguards who were waiting to save the woman who was then rushed to St Vincent’s Hospital.