There are two paper planes you could try this with:
Finding the plane:
One is at the very start when you leave the "building". The plane is laying on the table.
The second one is in a map called "Farm" (a street sign at an intersection shows the name and you can see it in the save file if you save your game there). You have to climb to the higher platform (there is a wind turbine up there) and walk the way that goes down to the end. There are also two small dinosaurs running around. At the end of the path is a piece of wreckage on the surface of which lies the paper airplane.
Throwing the plane:
You have to use your telekinesis to pick it up and use the "A"-Button (on Quest Controller) to throw it. If your get it to fly far enough you see the achievement poping.
BTW: The game keeps track over achievements. Even if it doesnt pop in Steam, you can see your success as a ingame HUD popup.