Seeing Wraith No. 4's vulnerable state and the fact that Bella didn't seem like she could finish the job, Adrian became a bit ambitious.
'What if...'
'What if he could kill him?' As this thought anchored itself in his mind, it refused to be dispelled. At first, he immediately rejected this idea. He was only a Foundation Establishment realm cultivator. There was no way he could kill a Nascent Soul realm cultivator.
But taking another look at Wraith No. 4, he ultimately decided it was worth a shot. Adrian was not an indecisive person. As soon as he made a decision, he began working on a plan to kill him.
He initially wanted to use another talisman, remembering how much damage it dealt to Wraith no 4 in the first place. However, he ultimately decided against it.
While he had quite a few of them, he couldn't recognise them. The Sage of Slaughter was not a Talisman master, so there was no knowledge about talismans left in the inheritance.