The brutal attack on the 20-year-old took place on Southsea Common on Wednesday at around 8.30pm.
Videos of the attack were shared all over social media yesterday.
Hampshire police told The News the woman was taken to Queen Alexandra Hospital with serious injuries to her head but she has since been discharged.
One video has been viewed nearly 600,000 times.
It shows three women fighting before one, wearing a mustard-yellow top and brown, spotted trousers, kicks a blonde-haired woman in the back – before stamping on the victim’s head three times.
Detective sergeant Jamie Palmer said: ‘This is a particularly vicious assault that has left the victim with serious injuries to her head and face.
‘Our investigations into what happened are ongoing and we would urge anyone who has information about what happened or any footage to contact us.
‘At this stage, we believe those involved are local to the area.’
The attack has been condemned by News readers and across social media as ‘sickening’ and ‘dreadful’.
One person said: ‘I was so shocked to see this video. I can’t understand how anyone could do this to another human being.’
Another reader said: ‘That's dreadful! I hope they arrest everyone involved and don't get away with a slap on the wrist. At their age they must know that stamping on someone's head can easily kill them.’
Another person added: ‘Made me feel physically sick. No matter what she did, no one deserves to be stamped on the head. That’s someone’s daughter, niece, maybe even mother! Disgraceful behaviour.’
Det Sgt Palmer added: ‘We know that there were a lot of people around at the time of this assault, so we want to hear from you to ensure those responsible are brought to justice.
‘We are aware of the footage posted online and would urge people not share this as this is causing extra distress to those involved. If you do have any footage please call us on 101, quoting 44200219951.
‘Our officers will be out on patrols on Southsea Common today, so if you have any concerns or any information which you think could help with the investigation, please speak to them.’