Feat of a Greek character — this writer participating in festival. say (11)
I believe the answer is:
achievement
'feat' is the definition.
(I've seen this before)
'a greek character this writer participating in festival say' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet).
'this writer' becomes 'me' (the person who wrote the clues).
'participating in' is an insertion indicator.
'festival say' becomes 'event' (festival is a type of event).
'me' going into 'event' is 'evement'.
'a'+'chi'+'evement'='ACHIEVEMENT'
'of' is the link.
(Other definitions for achievement that I've seen before include "Something done" , "Something accomplished; heraldic shield" , "Success" , "resulting in a coat of arms" , "Thing that is accomplished" .)