Robert McIntosh battered Linda McDonald, 52, as she walked her dog in Templeton Woods, Dundee in August, only running off when passers-by heard screams and rushed to help.
McIntosh, 31, had been let out of Castle Huntly prison for a week ahead of a parole board hearing when the attack took place on August 7.
He was jailed for 15 years in 2002 for murdering Anne Nicoll as she walked her dog on Dundee Law on August 2, 2001, stabbing her repeatedly.
McIntosh admitted attempting to murder Mrs McDonald when he appeared at the High Court in Edinburgh.
Mrs McDonald’s husband, Matthew, condemned the decision to allow McIntosh out on leave.
He said: “On August 7 a horrific and violent attack on my wife turned our family’s life upside down.
“Given his past conviction for a brutal murder I can’t believe the Scottish Prison Service deemed that this sick individual, who attempted to murder my wife, was allowed to be in the public domain.”
He added: “The fact that they did raises serious questions about the criteria followed by the appropriate authorities and if there had been strict monitoring, supervision and tagging in place we wouldn’t be going through this hell.”
Mr McDonald called on the SPS and the Parole Board to review release criteria and assessment systems as a matter priority, saying it was the “least we would expect”.
The court heard how McIntosh marched past Mrs McDonald in the woods before turning back to attack her.
Advocate depute Iain McSporran QC said: “He was expressionless as he passed her. After a few more steps his footsteps stopped and he ran up to her at speed.
“She turned to face him and saw him with his hand high above his head holding a metal object which has since been identified as a dumbbell.
“This was being brought down towards Mrs McDonald’s head. She raised her hands to cover her face and he brought the dumbbell down on her head.
“She described him as expressionless and he continued to strike her on the head and body. She was certain she was going to be murdered.”
Dog walkers Peter and Charles Connor, who had seen Mrs McDonald earlier, heard her screams and rushed to her aid.
They saw McIntosh crouched over something on the ground with a “vacant” expression on his face before he ran off.
They dialled 999 and stayed with Mrs McDonald until emergency services arrived.
She suffered two skull fractures and five head wounds in the attack and her thumb was broken in several places as she tried to defend herself.
Mrs McDonald has suffered dizziness and sleep deprivation since the ordeal and has not been able to return to work.
Solicitor Advocate Chris Fyffe, defending McIntosh, said his client felt “ashamed, contrite and penitent” about his actions.
Judge Lord Arthurson described the attempted murder as “one of the worst cases of violence I have had to deal with” and deferred sentence until November 22 pending reports.
The SPS said it would not comment on individual prisoners.
A spokeswoman said: “Those on home leave are released on license conditions. A rigorous risk assessment is undertaken prior to any offender being granted home leave. The majority of these take place without incident.”
But Scottish Conservative shadow justice secretary Liam Kerr said the case underlined the need for so-called “whole life” sentences.
He said: “If ever there were a case outlining the need for whole life sentences, this is it.
“This is an individual who killed a woman without remorse, but was set free 15 years later.
“If he’d been jailed for life – no ifs, no buts – he wouldn’t have been in a position to carry out this subsequent attack.
“The Scottish Government has to review this as a matter of urgency.”
A Scottish Government spokesman said: “This was a truly dreadful crime and while ministers can’t comment on the case, the guilty plea means that the individual responsible will be held accountable for his actions without subjecting the victim to further trauma during a trial.
“Processes for assessing and granting home leave are the most robust they have ever been and continue to be refined by the Scottish Prison Service. SPS have confirmed that a Critical Incident Review will be carried out following the conclusion of the trial to ensure that any lessons are learned.”