Hairdresser Jermaine McBride and a customer were attacked at her home at Woodside Heights in the Waterside area on Thursday morning.
Police have arrested two men, aged 32 and 37, in connection with the incident and the attempted robbery of a Credit Union in Donemana.
Mrs McBride said she felt lucky to be alive.
"He says: 'Give me your keys.' I said: 'I don't have any keys, my husband's got my keys,' and he just punched me in the face and I fell to the floor," she said.
"Then he just got on top of me and kept punching me in the head and in the face.
"I called the woman to phone the police but she couldn't because she was too nervous.
"She was holding a brush against him and I ran over to the neighbour and knocked on the door, and by the time I came back he had taken her bag and sped off."
The two men left the scene in the client's car, taking her handbag and mobile phone with them.
Mrs McBride said the attack has left her in pain and afraid to leave her own home.
"It was all so quick. He just pushed the door open and punched me and then I was on the floor.
"He lifted my head by the hair and kept punching me and I was just thinking: 'I'm going to die.'
"His eyes were bulging out of his head, he was just really really angry.
"I was covered in blood, my whole face was covered in blood.
"My nose is cracked and is really sore and my head's sore but it could have been worse. I really do feel unsafe in my home," she said.
"I always thought I would be a bit braver in situations like that, but I just knew if I had have even answered that man back I think I would have been killed.
"I'm trying to keep busy because every time I'm on my own I keep busting out in tears. I wouldn't stay in the house at the minute."

The federation said the demand for holiday homes in some English countryside districts was pricing locals out of the market.
It said new research showed Uttlesford in Essex saw the biggest jump in second homes between 2004 and 2009.
North Kesteven in Lincolnshire had the second biggest increase.
In Uttlesford, the number of registered second homes rose from 10 in 2004 to 214 in 2009.
North Kesteven saw a more subdued rise, with the number of second homes increasing from 128 in 2004 to 242 in 2009.
Aylesbury Vale in Buckinghamshire took the third place on the list with an increase from 217 holiday homes to 410 during the same period.
Other regions in the list's top 10 include Rushcliffe in Nottinghamshire, North Lincolnshire, north-east Derbyshire, Stratford-upon-Avon in Warwickshire, South Kesteven in Lincolnshire, Braintree in Essex and North Somerset.
The federation, which represents 1,200 housing authorities in England, said buyers were no longer just interested in the traditional second home hotspots of Cornwall, Devon and north Norfolk.
In a statement, its chief executive David Orr said: "Some areas of the English countryside have seen a huge rise in the number of properties being bought as holiday homes, which has pushed up prices beyond the level most local people can afford.
"If families and young people are priced out of their local villages it can have a hugely damaging impact on community life, with village shops, schools and pubs closing in alarming numbers as a result."
The research also suggested that the cost of an average home had risen in the last decade - from £175,278 in 2000 to £303,923 in 2009.
It also suggested there had been a rise in prices in the same period in North Kesteven - from £74,748 to £159,603.
The other areas are also suggested to have more than doubled in price in that time.
The organisation called for local authorities in such areas to create action plans which would tackle the situation.
Two women have been badly beaten during a hijacking in Londonderry.
[NEXT_CONCEPT]
Families are being forced out of their local areas as more buyers seek second homes in rural locations, the National Housing Federation has warned.