Street musicians are signified by a musical note icon on the minimap. They usually hang around street corners playing the guitar. They spook easily, so any flagrant use of powers will send them running (although kills after they drop their guitar and flee still count, you just lose the minimap icon to show where they are).
Any method of destroying them is valid, from melee hits and powers through to environment explosions and karmic streak (although that's possibly a little overkill!).
The count is cumulative, so just pick them off one by one as you progress through the game. You will get bad karma for these, so best done on an 'evil' play through.