Greek warrior cool in rising sea (8)
I believe the answer is:
achilles
'greek warrior' is the definition.
(I've seen this before)
'cool in rising sea' is the wordplay.
'cool' becomes 'chill' (similar in meaning).
'in' is an insertion indicator.
'rising' shows that the letters should be reversed in order (going up in a down clue).
'sea' reversed gives 'aes'.
'chill' inserted inside 'aes' is 'ACHILLES'.
(Other definitions for achilles that I've seen before include "Small but fatal weakness" , "Homeric hero" , "Greek hero with vulnerable heel" , "His heel was his weak point" , "Legendary hero with weak spot" .)