Authorities said Murphy was beaten to death in broad daylight on Wednesday around 4 p.m. while running along a canal dubbed Fiona's Way, named after Fiona Pender, a 25-year-old woman from Tullamore who vanished in 1996.
Local officials "continue to investigate the fatal assault" on Murphy and are "appealing for any information on a Falcon Storm mountain bike with straight handlebars and distinctive yellow/green front forks," An Garda Síochána, the national police service of Ireland, said in a Thursday tweet.
The Gardaí "are also appealing to anyone who was in the Cappincur/Canal walk area of Tullamore" on Wednesday.
Authorities initially arrested a 40-year-old man they believed was tied to the incident, but released him on Thursday, saying he is no longer a suspect, according to The Irish Times.
As officials continue to investigate the attack, Tullamore and other counties across Ireland have planned vigils and other tributes to Murphy. The phrase, "She was going for a run," has spread on social media since her killing, highlighting the unjust nature of her death and general violence against innocent women in Ireland.
Murphy's family remembered her as driven and loving in an interview with the Belfast Telegraph.
"The last thing she’d say in the morning going out was ‘Mam, I love you,'" her mother, Kathleen, told the outlet.
Her father remembered her as "a special girl," and the youngest in their family. "A little angel," he told the Telegraph.
Ireland's traditional music world also shared memories of Muprhy on social media, describing her as a talented and dedicated musician who traveled throughout Ireland to play.
"We are truly devastated by the tragic passing of our amazing friend and musician Ashling Murphy. Words cannot describe how heartbroken we are to lose such a special young lady, far too early in her life," Ballyboy Comhaltas, a traditional music organization, said in a Thursday Facebook post. "We are privileged to have had Ashling as a fiddle and tin whistle tutor within our branch. She had a warm and caring approach with her pupils and she inspired them to be the best they could be."
A Spar store in Tullamore remembered Murphy, who previously worked at the location, as someone who "always brought such happiness with her to work."
Helen McEntee, Ireland's Minister of Justice, said "every resource will be provided to An Garda Síochána to find who murdered Ashling Murphy" in a Friday tweet.
"It is vital that we all support the Gardaí in their work. Please anyone with any information, particularly on this Falcon Storm mountain bike, come forward to Gardaí," she said.
An Garda Síochána is asking anyone with information about the attack to contact (057 932 7600) or the Garda Confidential Line (1800 666 111).