The battered body of Courtney Herron, 25, was found by dog walkers in Royal Park in the inner Melbourne suburb of Parkville on Saturday morning.
Police say she suffered extreme violence – describing it as a "particularly horrendous attack".
Herron is the 20th woman to be killed in Australia this year, according to one count, and campaigners argue her death is part of a nationwide crisis of violence against women.
Henry Richard Hammond, a 27-year-old homeless man, has since been charged with her murder. He appeared in court on Monday, when his lawyer said he had mental health issues.
“There’s a diagnosis of possible delusional disorder, possible autism spectrum disorder and historical diagnosis of ADHD,” his lawyer, Bernie Balmer, said.
Mr Hammond was remanded in custody following his brief court appearance. His next trial hearing is in September.
Herron's death has provoked an upsurge of both fury and grief after a series of similar cases in Melbourne in the past year.
Her body was discovered just a short distance away from a different inner-city park where comedian Eurydice Dixon was raped and killed last June.
Public debate surrounding violence against women intensified after Ms Dixon's death and then exploded again just months later after 11 women died in violent circumstances around Australia during October.
"She died as a result of a horrendous bashing - that's the only way to describe it," Detective Inspector Andrew Stamper said of Herron's death.
He said her family had been left "heartbroken" – adding that she had experienced mental health and drug abuse problems and she had only "sporadic contact" with them.
He said that she was recently believed to have been "couch surfing with friends and possibly rough sleeping as well”.
Assistant Police Commissioner Luke Cornelius has said men's attitudes towards women must change in a speech to the press on Sunday.
He said: "Violence against women is absolutely about men's behaviour”.
The premier of Victoria state, Daniel Andrew, echoed his comments in a similar statement which said: "This is not about the way women behave ... this is most likely about the behaviour of men."
He has previously apportioned blame on sexist attitudes in the wake of other killings.
"It's understandable that people are very engaged when something strange and terrible happens in a park. But we have to recognise that this violence is not unusual - this happens to women every day in their homes," co-founder of Counting Dead Women Australia Jenna Price told SBS News.
"We know that every three hours a woman in Australia is hospitalised as a result of violence from a partner, a carer or a family member."
Since 2012, the Counting Dead Women project has researched and collated every "femicide" - the gender-motivated killing of women - nationally. Herron is the 20th woman on their list this year.The UN has said violence against women in Australia is "disturbingly common". According to government figures, one in five women, and one in 20 men, have experienced sexual violence or threats since the age of 15.
Almost one in three Australian women have experienced physical violence, and nearly one in five have endured sexual violence, according to recent Australian Bureau of Statistics figures. The rates are even higher for Aboriginal and Torres Strait Islander women.
Last week, a survey revealed one in five young Australian men believe that domestic violence is a normal reaction to stress. It also found one in seven young Australians - both men and women - think a man can force a woman to have sex if she initiated it but then changed her mind.
The National Community Attitudes towards Violence against Women Survey Youth Report found many young people have troubling views about sexual consent and abusive relationships in the country. It found one in three men believe women who say they were raped actually had consensual sex and later regretted it.
The study showed that while young people are increasingly in favour of equality in the workplace, they are less likely to identify sexism, coercion or other problematic behaviours within the context of their own relationships. The report surveyed more than 1,700 people across the country aged between 16 and 24.
Some 43 per cent of young people supported the statement: “I think it’s natural for a man to want to appear in control of his partner in front of his male friends.”