Shift register on Attiny85 programmed by Arduino Shift registers need 3 digital pins in order to work (data, clock and latch), but Attiny45/85 chips provides 2 digital and 2 analog pins.

Would I use 1 analog pin as digital pin? How?
The ATtinyX5 does not have any analog-only pins; all 5 pins are usable as digital I/O (all 6 if you know what you're doing, but if you need to ask how then you're not ready to do so).