In this page you can find a detailed description for unlocking "A Different Side of You" achievement in Prey. You get this achievement by scanning your Phantom Shift duplicate by using the Psychoscope. This achievement can be obtained only after acquiring the Psychoscope and unlocking one of the psychic powers (alien abilities).
You can get this achievement after buying the ability called Phantom Shift which becomes available for purchase after scanning Etheric Phantoms. In default you need to buy the second level of that ability, however, if you have a Psychoscope chipset called SpeedScan which allows you to scan faster (the picture above) then you can use the first level (this chipset can be found randomly in the game world).
Use Phantom Shift which creates your duplicate that appears behind your back. Turn around quickly and activate the Psychoscope so you can scan it and get the achievement (the picture above). Warning - If you weren't fast enough and couldn't scan it then you should buy the second level of said ability. However, if you have the SpeedScan chipset you don't have to upgrade the ability, the first level is plenty enough.