Lawyers for the family of Pearse Jordan claimed findings reached at the tribunal were unfair and should be quashed.
In a wide ranging legal challenge, they also contested a decision to deny them the chance to deploy parts of reports into so-called shoot-to-kill incidents.
A judge was urged to order a new inquest into the shooting.
Jordan, 23, was killed in disputed circumstances on the Falls Road, west Belfast in November 1992.
Witnesses claimed the RUC shot him in the back as he tried to flee after the stolen car he was driving was rammed.
His death was one of several high-profile cases in Northern Ireland involving allegations of a 'shoot-to-kill' policy operated by the security forces.
Last October a long-delayed inquest failed to reach agreement on key aspects.
The jury was split on whether reasonable force was used in the circumstances, the state of belief on the part of the officer who fired the fatal shots, and whether any alternative course of action was open to him.
They did agree that Jordan was shot by an RUC officer after he got out a red Ford Orion car which had been forcibly brought to a stop on the Falls Road.
Jurors also endorsed the findings of a post mortem examination that he died of a bullet wound to his chest.
Lawyers for the Jordan family were due to appeal against being refused permission to use reports into the 'shoot-to-kill' claims as part of cross-examination of three police witnesses at the inquest.
However, that challenge has now been included in a much more wide-ranging legal bid to have the jury's findings thrown out.
A two-day hearing to establish whether their application for a judicial review has an arguable chance of success is underway at the High Court in Belfast.
They want an order quashing the coroner's refusal to permit the next of kin to deploy narrative and analysis from the reports into six deaths John Stalker, the former assistant chief constable of Greater Manchester Police, and Sir Colin Sampson of West Yorkshire Police, investigated to try to establish whether police intended to kill.
Legal papers submitted as part of their case also focus on the jury and its findings.
The family is seeking a declaration that the coroner ought not to have accepted a verdict from a jury which was "hopelessly divided in circumstances where the verdict could not and did not determine any issue in contention".
They are also seeking a ruling that the failure to discharge the jury was a breach of the Coroners (NI) Act and a declaration that the coroner's decision to accept the jury's verdict was a failure to comply with human rights legislation.
It was further claimed that granting either anonymity or screening to security force witnesses undermined the effectiveness of the inquest, public confidence in it, and the next of kin's right to participate properly.
On that basis, counsel for the Jordan family argued that the tribunal was both unfair and unlawful.
The hearing continues.