The 18-year-old victim was punched in the face and fell to the ground after an argument broke out at around 10 pm.
She tried to escape but was followed to the Parade and heckled by the two girls.
The same girl who had punched the victim at the People’s Park then lunged forward and punched her in the face again.
The girl again fell to the ground and was holding her bleeding nose while lying on the grass opposite the Hospital.
She took herself to A&E and was treated for a suspected broken nose.
A police spokesperson said: ‘This was a nasty assault that left an 18-year-old girl needing hospital treatment and we would urge any witnesses or anyone with information to call police headquarters on 612612 or call Crimestoppers anonymously on 0800 555 111.’