This badge seems to be awarded when you vote to delete a proposal, yet it says:
First vote to delete a question.
Maybe this should be corrected?
I am not sure that badge is referring to delete a proposal, as that requires a reputation of at least 200, while there are users with a lower reputation, and that badge. I have that badge too, and I have never voted to close a proposal.
I think it is really referring to the questions for a proposal, when the old system was used.