In the run-up to the airline's annual shareholder meeting this week, investors have been urged to vote down excessive bonus payouts and block eight senior bosses from re- election.
The London-based Pirc advisory group called for a shareholder revolt at Europe's biggest airline due to concerns over the independence of the board.
It did not recommend against the re- election of the chief executive.
Stan McCarthy and seven other Ryanair non-executive directors have been advised to vote against the re-election of them.
The reason for non- independence was the award of share options to most of the directors in previous years.
The independence of other non-executives was at risk because they had been senior bosses at the airline before being elevated to the board.
There wasn't enough independent representation on the board of the company.
It called for votes against the pay policy which it said could lead to excessive variable remuneration.
The most notorious plank of the policy is the share option scheme, which gave O'Leary a potential 99m bonus if he could double the market value or profits in the next five years.
The restoration of a bonus that took O'Leary's earnings back to pre-pandemic levels of 975,000. While other staff are on reduced Covid pay, the pilots union has criticized his pay as morally bankrupt.
The handling of sick pay and misleading advertisements featuring the UK vaccine rollout that were not considered to meet best-practice standards could be potentially harmful to stakeholders and should lead to the ousting of O'Leary.
The advisory group has softened their stance on O'Leary after he improved his reputation in the UK with a low number of canceled flights and few problems because of labour shortages.
Last month, the airline carried a record 16.9 million passengers, bringing its yearly total to over 150 million.
The company will hold its annual meeting at its engineering base near its head office.