I would say there is very little violent crime in Sofia.
The worst you can get see is usually a brawl outside a nightclub/pub or a road rage accident. There is also a bit of a problem with football hooligans / skinheads, but those tend to be very isolated. I've lived my whole life in Sofia and have felt much more secure here than in some places in the UK.
Of course, as with many places, foreigners tend to be a target more often for criminals, but I've never really heard of an armed robbery or anything of the kind against a foreign citizen living in Sofia.
Hope this helps.