Attiny13 project with leds and electret microphone
want to use 1 electret microphone instead of the buttons.


In what way do you want to use the microphone? You do realise, don't you, that an Arduino can't understand speech (or much of anything really) without powerful extra hardware? A microphone by itself is pretty much useless, especially without any form of preamp and signal conditioning.


  i only want to know if it is possible to make the project with the attiny13a chip without the requirement of any additional parts.


No, it's not possible. You will require lots more parts. You can't just take an arbitrary chip and connect it to a battery and expect it to work properly. You need to consider correct supply voltages (voltage regulation or boosting depending on your power source), decoupling capacitors, drive circuitry, amplification, signal processing, etc...


  i wanted to use these leds instead of the lilypad led's, so i want to know if i can do the model in exactly the same way without using any mofsets etc


Again, no.  Those are 12V LED strips. You need both a 12V supply (and the associated regulation down to 5V to power the ATTiny etc) and MOSFETs (or something similar) to allow the ATTiny to switch that 12V to the LED strips as needed.