Whistle-blower's story about Archer? (4)
'whistle-blower's' is the definition.
(thesaurus)
'story about archer?' is the wordplay.
'story' becomes 'tale' ('tale' can be a synonym of 'story').
'about' means one lot of letters go next to another.
'archer?' becomes 'tell' (I've seen this before).
'tale' put after 'tell' is 'TELLTALE'.
(Other definitions for telltale that I've seen before include "Person who blabs, or something revealing" , "Informer - monitoring device" , "One spreads other people's secrets" , "Gossip-monger" , "Blabbermouth, snitch" .)
'archer?' is the definition.
(I've seen this before)
I can't explain the remainder of the clue.
(Other definitions for tell that I've seen before include "Count - recount" , "Order" , "Make a difference" , "Make an impact" , "Instruct" .)