He was declared fit to plead by the Court of Appeal before admitting the charge of killing Edwards.
Akuhata had four previous convictions for male assaults female, three of which involved Edwards.
Akuhata and Edwards had been in an "on again, off again" relationship for about six and a half years.
But when Akuhata murdered her, they were apart and there was a protection order in place for Edwards and her two daughters.
One night in July 2012, Edwards agreed to go to an event at a bar with Akuhata. During the night, he became angry at Edwards about text messages she had received.
According to facts accepted at the time, they left the bar about 1.55pm and were arguing on the Lower Tarewa Rd bridge when he lifted her up and over the railing into Waiarohia Stream.
He then grabbed her hair and held her head under the water until she stopped showing signs of life.
He went home where he told a family member Edwards was dead.
In court in Wellington today, human rights lawyer Tony Ellis questioned Akuhata's previous lawyer, Catherine Cull, suggesting she did not try to run a defence for Akuhata and did not handle his case correctly, given his brain injury.
He asked whether there had been some pressure on "a brain injured person" to plead guilty.
But Cull said she had several discussions with Akuhata about the guilty plea and he was "keen" to enter it. She said she gave him plenty of time to think about it first.
Ellis told the panel of judges Akuhata didn't want to plead guilty to murder before the brain injury, and there must have been some type of pressure on him to do so.
He said cases like Akuhata's should be appointed one judge specially trained in dealing with "vulnerable defendants".
The judges have reserved their decision.
