Board Thread:Questions and Answers/@comment-24.62.142.87-20140331201702/@comment-1173941-20150428013600

Hah? Don't know where the comment about Reki "didn't leave anything out". He's missed a number of things, and there are questions here and there. As for Elucidator, if you look at the article, there's a citation of where it was mentioned. Volume 10, Chapter 4, Part 3.

Anyways, I think we've discussed this before on the wiki, but the text didn't specify if it was the main floor boss or not. Or rather, we decided it was too ambiguous to tell for sure. Here's a fan-translation of the line:

On the 50th level, when I held the black longsword «Elucidator» the boss dropped.

Simply put, SAO doesn't have just a single boss for each floor. The only ones that are important for clearing the game are the Field Bosses and the Floor Bossed. But there are also Dungeon bosses, like the Fatal Scythe. So all we know is that Elucidator was dropped by a Boss monster on the 50th Floor.