The world champion kayaker and his younger brother Dru Baggaley were each found guilty last year of attempting to import up to $200 million worth of cocaine into the country.
Nathan Baggaley is serving a 25-year jail sentence for his role, while Dru, 40, was sentenced to 28 years behind bars.
Queensland Appeal Court judges are yet to hand down their decision on the appeal against Nathan Baggaley's conviction after a hearing in March.
But on Friday, the 46-year-old represented himself in applying for the appeal to be re-opened, telling the court sitting in Brisbane his lawyers failed to follow his instructions.
It was "incompetent to say the least" that his legal counsel had not argued certain aspects during the earlier appeal proceedings, he said.
"Not once in the previous hearing did they use the words 'false line of reasoning'.
"For my legal counsel not to advance that argument and not to even raise that point I feel is incompetent."
When an Appeal Court justice stated Baggaley was represented in the hearing by "one of the most experienced criminal barristers in Queensland" Michael Copley, Baggaley replied: "I recognise that, and can I just clarify here as well, I'm not here criticising Mr Copley.
"I believe Mr Copley was not properly instructed by his juniors."
Baggaley argued about the trial prosecutor's claim he communicated or tried to communicate with his brother at sea using the pseudonym "Thunderbutt" saying: "I'm on standby, ready".
"I believe there's been a misapprehension of the facts regarding the whole Thunderbutt circumstance."
During a sometimes heated discussion, Justice David Boddice said Baggaley's evidence during the trial had obviously been rejected by the jury.
The former sportsman responded that he was in court to argue the jury verdict was unreasonable.
But Justice Boddice said the Appeal Court hearing was only an opportunity for Baggaley to "point to something that is new".
"To put it in the vernacular: You don't get to fire the dog and do your own barking," Justice Philip Morrison said.
"You had a very experienced barrister to run your appeal, so you don't just get to run it differently because you think you could have done better."
The trial heard Baggaley played an "essential role" in the attempted importation, buying the rigid-hulled inflatable boat (RHIB) used, a trailer and equipment like a satellite phone and GPS system, all worth more than $100,000.
His brother was found to be "a principal organiser" of the plot and recruiter of another man, Anthony Draper, to go to sea with him.
Draper and Dru Baggaley set off on the RHIB from Brunswick Heads in July 2018, meeting a foreign freighter about 360 kilometres off Queensland's coast about 11 hours later.
The men retrieved packages thrown off the other ship, but on their return flung them into the sea when pursued by an Australian navy vessel.
Bundles recovered at the time, together with those that washed ashore for months after, contained 650 kilograms of white powder containing cocaine worth between $130 million and $200 million.
The two men were arrested before they reached the mainland and Nathan Baggaley was arrested almost a year later.
The brothers told the trial the boat was for a whale watching business they intended to start.
The Crown argued earlier there was no evidence of steps taken toward setting up the commercial venture, aside from buying the boat.
The three appeal court judges reserved their decision.
