Greek hero cool in rising sea (8)
I believe the answer is:
achilles
'greek hero' is the definition.
(I've seen this before)
'cool in rising sea' is the wordplay.
'cool' becomes 'chill' (synonyms).
'in' indicates putting letters inside.
'rising' says the letters should be written backwards (going up in a down clue).
'sea' reversed gives 'aes'.
'chill' placed within 'aes' is 'ACHILLES'.
(Other definitions for achilles that I've seen before include "Legendary Greek with bad heel" , "Greek hero who gave his name to a bad heel" , "Greek hero (with heel and tendon)" , "great hero" , "& 22 Person's vulnerable point" .)