The claim is mostly true because Barack Obama was indeed presented with the Freedom of the City of Dublin, which is a prestigious civic honor, and he received a first edition of James Joyce's Ulysses as a gift during the ceremony; however, the claim incorrectly calls this the 'Dublin Medal of Freedom,' which is not an official award name and should not be confused with the U.S. Presidential Medal of Freedom.
President Obama received the Dublin Medal of Freedom, and a First Edition of Ulysses.

Former US President Barack Obama presented with the Freedom of the City of Dublin - Dublin City Council
Source: dublincity.ie
Key Evidence
Multiple sources including Belfast Telegraph, Irish Star, Dublin City Council, Irish Post, and Irish Mirror confirm Obama received the Freedom of the City of Dublin.
These sources also report he was presented with a first edition American edition of Ulysses by James Joyce as part of his gifts.
The Presidential Medal of Freedom is a distinct U.S. Award unrelated to this Dublin honor (Wikipedia).
What the Evidence Shows
Multiple independent sources confirm that former President Barack Obama was awarded the Freedom of the City of Dublin in a formal ceremony. This honor is Dublin's highest civic award, given to individuals who have made outstanding contributions and whose values align with those cherished by Dubliners. During this event, Obama signed the Roll of Honour and was presented with several gifts, notably including a first edition American edition of James Joyce's Ulysses and a bottle of Dublin Whiskey by Teelings. These details are consistently reported across reputable Irish news outlets and official Dublin City Council communications.
However, it is important to clarify that the 'Freedom of the City' is distinct from the 'Presidential Medal of Freedom,' which is a separate and unrelated U.S. Civilian award bestowed by the President of the United States. There is no evidence that Barack Obama received any award called the 'Dublin Medal of Freedom.' The phrase in the claim appears to conflate or misname the actual honor he received.
Therefore, while Obama did receive a significant honor from Dublin and was gifted a first edition of Ulysses, calling it the 'Dublin Medal of Freedom' is inaccurate. The correct terminology is 'Freedom of the City of Dublin.'