As I have said before Russian is not my first language and this isn't an easy one to translate but I did what I could:
F: You're not worried about it at all.
F: Why are you picking on me? Leave me alone please!
Dima (attacking): Whore! Animal! What don't you like?
D: What? Does it hurt?
D: Who do you think you're talking to? [He uses the present tense but is referring to something said before the film.]
D: What do you think?
(F2 enters)
D: Get out of here!
D: (unintelligible, something about someone's father)
D: I don't give a fuck about you or your family! Who do you think you're talking to?
(F2 enters)
F2: Dima, stop!
Dima: Get out of here!
D: Who the fuck do you think you're talking to (something about someone's father again), haven't you got someone mixed up?
D: Bitch! (approximate translation, there isn't a good translation for this word in English in this context)
D: Haven't you got mixed up, scum?
D: [I struggled with this bit] Why are you alive cunt? Stupid cunt!
M2: Dima, Dima!
D: Get out of here!
M2: Dima, please!
Anyone can auto translate text now and soon the IT will put me out of business on translating speech as well but the article says the woman, who is a barmaid, has multiple skull fractures and other injuries. It also says Dima has not been caught yet (at the time of writing) and that he was harrassing the barmaid and called her a terrorist and 2 men tried to calm him down. That wasn't on the clip on that site so there must be a longer video.
Barmaid was probably verbally and psychologically tormenting and disrespecting him, secure in the knowledge that he couldn't do anything about it and there might be some reference to her or his child, it's not clear what father he's referring to.