You'd be forgiven for thinking this achievement requires some sort of special setup, but in fact it's story related and cannot be missed.
Like previous devices, such as the connector, the hexahedron and the recorder, the "platform" is an unlockable item required for progression. It can be found in the cathedral, (building C).
Once you've unlocked the device, look for any puzzle in world C that has an icon which matches the achievement picture of a guy holding the platform above his head and the "play" icon indicating the presence of a recorder.
In the puzzle, set the recorder going and pick up the platform. Walk towards a low ledge or a hexahedron, and stand there for ten seconds. Drop the platform and switch off the recorder.
Now, go and stand on the ledge/hexahedron, and when your recording arrives, jump onto the platform it's holding.