Dust follows Isaac and is only visible when in close proximity to him. Dust will speed up when close, but damaging it will cause it to teleport away, typically around corners of the room. They are immune to damage when invisible.
After taking any amount of damage, they will stop for a bit and then teleport away. The general strategy to kill them is to apply as much damage as possible in this small time frame. Items such as Monstro's Lung, Chocolate Milk or Brimstone will allow Isaac to discharge charged up damage at the right time.