Marian Clode (formerly Coyle) from Glasgow Terrace in the Rosemount area of the city, was on holiday with her family when it happened on 3 April.
The teacher had been living in Ashton-under-Lyne, in Greater Manchester.
Her daughter, Lucy Rowe, said her mother, who was 61, had been "flipped like a ragdoll" over a fence.
Mrs Clode and her husband, daughter, son-in-law and two grandchildren had been walking along a public path through farm land when the incident happened.
The family said one of the animals approached Mrs Clode and "repeatedly headbutted" her.
"It flipped my mum like a ragdoll over the fence that she was stood up against and into the next field," said Mrs Rowe.
"In the words of the consultant, the injuries that my mum had sustained.... were worse than any that they had ever seen and only equivalent to a high speed crash.
"Immediately, her lips went blue and I was screaming her name."
Lucy Rowe's husband, Kevin, said: "I could see the cows at the top of the hill and I could see they were really running fast.
"I'll never forget the sight of that bull, or aggressive cow, scraping its legs."
Mrs Clode was airlifted to the Royal Victoria Hospital in Newcastle but died two days later.
The Health and Safety Executive have confirmed that an inquest into her death is under way.
An inquest is under way into the death of a woman, originally from Londonderry, who was attacked by cattle in Northumberland.