Prey

In order to mimic an object, you'll need to progress through the main story until you are given a psychoscope. Use the scope (click right stick) to scan mimics until you unlock the Mimic Matter ability, then purchase it with 3 neuromods.

Once you have the ability, use your favorites wheel (hold down Y) to select it, hold left trigger, look at a small object, and release the trigger while the object is highlighted to shapeshift into it. Unlocking the upgraded versions of the ability will allow you to mimic a greater variety of objects. The achievement will unlock once you mimic 20 different types of object.

Here's a tip to unlock this very quickly: If you're anything like me, your inventory is full to the brim most of the time with food and junk items. Every single thing you can carry in your inventory is a valid target for Mimic Matter I, so you can dump everything on the ground and spend some time (and psi hypos) mimicing each object 1 by 1 to snag the achievement with little effort.