Daniel James Holdom has been in custody since November 2018 after pleading guilty to the murders of Karlie Pearce-Stevenson, 20, and her two-year-old daughter Khandalyce Pearce 10 years earlier.
Ms Pearce-Stevenson's remains were found in NSW's Belanglo State Forest in 2010, but were not identified until her daughter's remains were discovered five years later in a suitcase dumped beside a South Australian highway.
The sentencing judge highlighted the "appalling depravity" and "very great heinousness" of the murders and noted Holdom had shown no remorse.
But Holdom, now 51, claims the sentences imposed on him are "manifestly excessive" and is pushing for a lesser sentence in a severity appeal filed with the NSW Supreme Court.
He argues Justice Robert Allan Hulme erred by failing to properly take into account his pleas of guilty, which he tried to withdraw on the morning of his sentencing.
Offenders can receive a discount for the utilitarian value of entering guilty pleas at an early stage at the discretion of the judge.
Sentencing judges are required to give proper consideration to an offender's subjective factors, such as their background, which Holdom alleges Justice Hulme failed to do.
"The offender's culpability is so extreme, and that his crimes are of a level of heinousness, that no objective or subjective factor(s) mitigates the need to impose the ultimate sentence," Justice Hulme found at the time.
The third pillar of Holdom's appeal is that the judge erred when rejecting the professional assessments of him by a forensic psychiatrist.
In his decision, Justice Hulme said he could not rely on the psychiatrist's opinions in part because he appeared to accept an inaccurate and deficient account from the murderer.
The appeal was first mentioned in court on Thursday, when it was set down for a two-hour hearing on March 18.
It comes seven years after the public gallery of a courtroom erupted in applause as Holdom was jailed for two lifetimes.
He was found to have violated Ms Pearce-Stevenson "in a most callous and sadistic way" by violently murdering and sexually assaulting her before abandoning her half-naked body in the forest.
"His treatment of her showed complete disdain for her existence as a human being," Justice Hulme said.
"To him, she was just flesh with a life that could be extinguished for his vile pleasure."
Four days later, Holdom carried out the "despicable" murder of a "completely defenceless" Khandalyce, whom he accepted he tried or planned to sexually assault.
He stuffed a dishcloth in the toddler's mouth and wrapped a disposable nappy around her head before putting her body in a suitcase.
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