Originally Posted by Milk Viper
No, you just had to actually received them for the items to count for the achievement. After that you can sell or toss them in the ocean.
I've had all sixteen Items in my inventory from the below list at one time & still not been given it yet?
Azura`s Star, Dawnbreaker, Ebony Blade, Ebony Mail, Mace of Molag Bal,
Masque of Clavicus Vile, Mehrunes`s Razor, Oghma Infinium, Ring of Namira, Sanguine Rose, Savior`s Hide (NOT Ring of Hircine), Skull of Corruption, Spellbreaker, Volendrung, Wabbajack & Skeleton Key
I know the key doesn't count so as it didn't dish out the achievement, i've had to start a new playthrough just for this not that its an issue.