The definition for the "Oblivion Walker" achievement is "Collect 15 Daedric Artifacts". However, this does not specify whether the player must simultaneously own all 15, or if they must simply at one point in the game have collected them.
For example, let's say I've completed The Whispering Door and obtained the Ebony Blade. Later on, not thinking of this achievement's requirements, I decide to sell or otherwise dispose of the artifact, in a way which causes it to be non-recoverable to me. Can I still gain the achievement if I go on to collect the rest of the artifacts?