Following achievement the lady’s down (a bit) (7)
I believe the answer is:
feather
'down a bit' is the definition.
'feather' can be an answer for 'down' (thesaurus). I am unsure of the 'a bit' bit.
'following achievement the lady's' is the wordplay.
'following' says to put letters next to each other.
'achievement' becomes 'feat' (feat is a kind of achievement).
'the lady's' becomes 'her' (belonging to a lady).
'feat'+'her' is 'FEATHER'.
Can you help me to learn more?
(Other definitions for feather that I've seen before include "Free hat (anag)" , "thing of little importance" , "In your cap, it's an accomplishment" , "Rotate (propeller) blades (to reduce thrust)" , "English plume (de ma tante?)" .)