First, suck out all the cyclones individually with your most powerful vacuum, something like a DC14 or a Henry would be good.
If that doesn't work, let the cyclone soak in hot water and bleach for a few hours so all the dirt just turns to gunk and spills out.
If that doesn't work, get a sink unblocking powder which (BTW you need to wear protective gear with), so justpour that powder into the cyclones and then pour boiling kettle water into thta, it should eliminate any hair etc.