How delay or phase shift a signal?
Ok, so that circuit builds the common 555 square wave oscillator and drives an emitter follower from the capacitor voltage.  The emitter follower drives the LED.

To get the multi-stage throbing build first a circuit that produces multiple phase-shifted square waves - for example build a ring counter ans drive the clock input using the 555 - then smooth the edges of the pulses from the ring counter with the resistor-capacitor-transistor combination that the throbbing circuit uses.  Use a smaller resistor or capacitor on the 555 as it will need to run faster in this application.