The Police say it involved five people, and took place between 22:15 and 22:45 on Friday night, starting in King Street.
The group – three men and two women – began arguing, before moving into the Royal Square.
An assault was then alleged to have taken place near the entrance to the Royal Court, followed by another at Library Place outside Barclays Bank.
Moving through Bond Street, the fight then culminated in what Police described as a “violent attack” involving two of the men in Mulcaster Street, in which one used a pole as a weapon.
A 24-year-old and 27-year-old were arrested on the night following the alleged incident, but were later released on bail.
Police have since described the incident as a mix of an “affray”, “grave and criminal assault” and “possession of an offensive weapon.”
Anyone who witnessed the alleged assaults is asked to contact Police on 612612 or anonymously speak to Crimestoppers on 0800 555111.