Robin2:
To make the Attiny into a USB-TTL adapter you would need to write a program that can handle raw USB I/O. That is a complex process and my guess is that if you know how to do it you would not have to ask a question here.
V-USB has that as an example sketch.
But before you do it: Go to google and search for "tiny85 software serial". Count how many results say "it works!" and how many say "it doesn't work!"