Melbourne women Amanda Warren, 32, and Caris Underwood, 20, appeared before Victoria's County Court on Thursday to appeal the sentences they received for the March 2016 attack.

A magistrate in December ordered Warren serve eight months in prison and Underwood four but shortly after, they were released on bail as they appealed their sentences.

Lawyers for the women on Thursday said the'd had tough childhoods but had turned their lives around since drunkenly assaulting paramedic Paul Judd at Reservoir.

Details of Underwood and Warren's childhoods cannot be published for legal reasons but prosecutor Stephen Devlin acknowledged they had endured "very unfortunate upbringings".

He said their rehabilitation was just one of the factors judge Barbara Cotterell should consider as she contemplated their appeal.

"Attacks on emergency workers have been identified as being far too often," he said.

"That's why parliament has made it clear that this is a circumstance where mandatory sentence can be applicable."

Mr Devlin also said deterrence was an important factor in deciding the appropriate sentence for Underwood and Warren's crime, which judge Cotterell described as "terrible".

"The attack is shocking," she said.

"But are these girls - who have had very unfortunate lives, I have to concede, and have psychological damage from that - are they appropriate vehicles for general deterrence?"

"That's the big question for Your Honour," Mr Devlin said.

The women had pleaded guilty to intentionally causing injury, with Warren also pleading guilty to handling stolen goods after a gold necklace was ripped from Mr Judd's neck.

Their sentences marked the first time a mandatory minimum jail term had applied for the assault of a paramedic.

Victorian laws introduced in 2014 require anyone who intentionally injures an emergency worker to be imprisoned for at least six months, unless there are "special reasons".

Underwood's age, being 18 at the time of the attack, was considered a special reason.

Counsel for Warren, Cecily Hollingworth, said her difficult childhood and a mental impairment also constituted "special reasons".

"It's accepted that Warren has impaired mental function ... linked to what happened to Mr Judd," she told the court.

Mr Judd was repeatedly punched and left with a broken foot while he and a colleague tried to treat an unconscious man.

The paramedic of more than 40 years needed three operations and has been unable to return to work.

Judge Cotterell will hand down her decision on Tuesday.

Australian Associated Press