When the app starts, press to move over to ‘Library’ and select ‘Interactive Episodes’.
This is unlocked at the start of any episode. You must start at the beginning of the episode and not a chapter.
When Cooper asks you to stand in the mirror, just stand there and he will disappear to change his clothes (presumably to what you are wearing). That’s it.
When this section is over and the next chapter starts, just press , move over to ‘Stop’ and press again. The achievement will unlock when it is buffering.