I imagine you are trying to turn on 1 LED at the time up to 20 and start again, if so this is one way to do it.
You will need the 555 to give you pulses to drive the shift register the pulses will determine how fast the LED's will shift
Use a 2 4017 is series to give you 20 steps set up as a ring then connect each Q output to a ULN 2004 and the output of the 2004 will be connected to the LED's
Since only one LED will be on at the time only one current limiting resistor could be used in series with the supply voltage at the ULN2004. At the point I would say that you do not need the LM2577 the circuit should run on 5 volts, depending on the LED's you are using 200ma at the supply should do the job.
Depending on you electronic knowledge you may need to do a bit of reading on the components and how they are connected together.
You will need the 555 to give you pulses to drive the shift register the pulses will determine how fast the LED's will shift
Use a 2 4017 is series to give you 20 steps set up as a ring then connect each Q output to a ULN 2004 and the output of the 2004 will be connected to the LED's
Since only one LED will be on at the time only one current limiting resistor could be used in series with the supply voltage at the ULN2004. At the point I would say that you do not need the LM2577 the circuit should run on 5 volts, depending on the LED's you are using 200ma at the supply should do the job.
Depending on you electronic knowledge you may need to do a bit of reading on the components and how they are connected together.