If you have 5v power source you do not need to build the LM7805 Voltage regulator circuit as in the drawing.

Code

Download TM1637 Library: https://github.com/lpodkalicki/attiny-tm1637-library/ and put files in same folder with code.

Arduino code:

That how long is 1 second may need manual calibration. For now it is 90m/s.

_delay_ms(90); //

My tutorial how to setup Arduino and upload code: https://www.hackster.io/taunoerik/programming-attiny13-with-arduino-uno-07beba

/*
* ATtiny timer with TM1637 display
* Tauno Erik
* 18.02.2018
* 
*/
#include <stdint.h>
#include <avr/io.h>
#include <util/delay.h>
#include "tm1637.c" 
int main(void)
{
 uint8_t    i = 0; // Display 1 num right to left
 uint8_t   ii = 0; // Display 2 num right to left
 uint8_t  iii = 0; // Display 3 num right to left
 uint8_t iiii = 0; // Display 4 num right to left
 PORTB |= (1 << PB4); // enable start/stop button
 TM1637_init(); 
 while (1)
 {
 int BUTTON = PINB;
 if(!(BUTTON&0b00010000)){
   /*When Button is ON */
   // Display 1 num right to left
   TM1637_display_digit(TM1637_SET_ADR_03H,i % 0b00001010);
   // Display 2 num right to left
   if(i > 9 && ii==0){
     ii = i-9;
     TM1637_display_digit(TM1637_SET_ADR_02H, ii % 0b00001010);
     i = 0;
   }else if(i > 9 && ii > 0){
     ii++;
     TM1637_display_digit(TM1637_SET_ADR_02H, ii % 0b00001010);
     i = 0;
   }
   // Display 3 num right to left
   if(ii > 9 && iii==0){
     iii = ii-9;
     TM1637_display_digit(TM1637_SET_ADR_01H, iii % 0b00001010);
     ii = 0;
   }else if(ii > 9 && iii > 0){
     iii++;
     TM1637_display_digit(TM1637_SET_ADR_01H, iii % 0b00001010);
     ii = 0;
   }
   // Display 1 num right to left
   if(iii > 9 && iiii==0){
     iiii = iii-9;
     TM1637_display_digit(TM1637_SET_ADR_00H, iiii % 0b00001010);
     ii = 0;
   }else if(iii > 9 && iiii > 0){    
     TM1637_display_digit(TM1637_SET_ADR_00H, iiii % 0b00001010);
     iiii++;
     iii = 0;
   }
   _delay_ms(90);//
   i++;
 }else{
 /*When Button is OFF */ 
 }
 }//while loop end
}//main end

Demo: