Ahead of his first trial in 1994, Pora confessed to police. Doubts then began to emerge about the case and Pora was granted a re-trial in 2000, but was again found guilty.
Mr Krebs said Pora had recently been diagnosed with a fetal alcohol disorder, which raised doubts about whether he understood what he was confessing to.
"It will be argued that the confessional material is so demonstrably unreliable that it ought to have been taken away from the jury."
Without that, there was no forensic evidence to place Pora at the scene of the crime, Mr Krebs said.
After Pora's first trial, serial rapist Malcolm Rewa was convicted for raping Ms Burdett.
His DNA was found at the scene and at Pora's re-trial the Crown argued the two acted together.
But Mr Krebs said that ignored the fact they were associated with rival gangs and that Rewa had an erectile dysfunction problem.
That the re-trial jury was not told of Rewa's problem was down to error on the part of Pora's then lawyer.
Crown lawyer Matthew Downs said there were doubts about the expert evidence Mr Krebs had obtained on false confessions.
And of the five grounds of appeal put in front of the Privy Council, the law lords had not accepted three.
Justice Lang suppressed other parts of the discussion and reserved his decision on bail until next week.
Pora will also have a parole hearing at the end of the month but Mr Krebs has said he would prefer Pora to be bailed as people on parole can be recalled to prison instantly.
