Without success (6)
(Other definitions for vainly that I've seen before include "How conceited people might act" , "Without success, ineffectually" , "To no avail" .)
'without success' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for in vain that I've seen before include "Without success or result" , "Uselessly, to no avail" , "Fruitlessly" , "Without effect" , "Uselessly, without any progress" .)