Police have identified the woman whose body was found at Royal Park in Melbourne's inner north.
She's been identified as Courtney Heron, a 25-year-old woman of no fixed residence.
In a press conference, Homicide Squad Detective Inspector Andrew Stamper said she had been couch surfing and sleeping rough.
W e do have a result from the post-mortem examination that revealed she died as a result of - a horrendous bashing - that's the only way to describe it," he said.
Police believe she was assaulted at the scene sometime between Friday night and Saturday morning.
Detectives have not established the circumstances leading up to her death but say her last confirmed sighting was in St Albans in Melbourne's west.
Detective Inspector Stamper said she was known to have had issues with drugs and mental health.
"As we are all aware, homelessness is often a factor that goes with those two challenges in life," he said.
It comes as Premier Daniel Andrews said men's attitudes to women need to change as Melbourne grapples with another tragic death of a woman.
Her body was found in Royal Park by dog walkers on Saturday morning, while her killer remains on the loose.
"This is a terrible tragedy," Mr Andrews told reporters on Sunday.
The Premier, who delivered Australia's first royal commission into family violence last term, said while the state had made significant progress on violence against women, there was more to be done.
"This is not about the way women behave, this is not about where women are at what hour," he said.
"This is most likely about the behaviour of men."
It's a sentiment echoed by Assistant Commissioner Luke Cornelius, who told reporters earlier that Melbourne was a safe city but attitudes against women needed to change.
"What is it in our community that allows some men to think that it's still OK to attack women or take from women what they want?" he said.
"Violence against women is absolutely about men's behaviour."
Detective Inspector Andrew Stamper said earlier officers were trying to work out how she was killed.
"Sadly at the moment we still don't know who this female is, we don't know the circumstances that brought her to the park or what happened," he said.
He said police had no idea yet of the woman's age, cause of death or if they're looking for a particular weapon, but suggested the possibility it was a random attack would be a "strong focus".
Pathologists arrived yesterday afternoon, while SES crews are expected to join police for a line search. CCTV is also being collected.
The park is one of Melbourne's busiest by day and used by rough sleepers at nigh and police have appealed for anyone who saw anything on Friday night or the early hours of Saturday to come forward.
It is also a short distance from Princes Park, where aspiring comedian Eurydice Dixon's body was found on June 12 last year.
The death is the latest in a series of women killed and dumped on Melbourne's streets since Ms Dixon's rape and murder.
Aiia Maasarwe, 21, suffered a similar fate to Ms Dixon after being attacked on her walk home near La Trobe University on January 15.
Both women were attacked by men they did not know.
Jaymes Todd, 19, has pleaded guilty to the murder and rape of Ms Dixon and will return to court in August, while Codey Herrmann, 20, has been charged with attacking Ms Maasarwe.
And in April Natalina Angok's body was found dumped in Chinatown, allegedly killed by her one-time partner Christopher Allen who has been charged.
Detectives say they're in need of any piece of information the public can provide.
A heavy police presence will continue in the park in the coming days, with mounted police and officers on bikes to patrol the area.
"This is a horrendous crime, as all murders are, and particularly the murders of women and we've got our best people [investigating]," Detective Inspector Stamper said.
"Our focus as always will be on catching the perpetrator of this horrendous crime and I give the community my assurance that we won't stop."
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