Legolas informed Edmund, their ally in this expedition that they had killed the boss and not even its body was left.
But in reality… Armin had gathered all the chunks of flesh, extracted the blood and bones under Kahn's orders. To remove the evidence of the fight and how they killed the boss.
Legolas also told Edmund that the boss had a mental attack skill that targeted him, the weakest of the group, and made him faint. Thus, he was knocked out during the whole battle.
As for how they killed it?
He iterated a fake battle strategy with some truth to it such as surrounding and overwhelming the boss with numbers.
Because in the end, killing a mythical rank boss was a great feat so they didn't want the alchemist to ask unnecessary questions that could unravel their secrets.
The more oblivious Edmund was about their true battle prowess, the better.
All in all, they were now free to leave this floor and progress further.