The most common and most likely answer to this crossword clue is the 8 letter word ODYSSEUS
O
D
Y
S
S
E
U
S
More clues leading to the result ODYSSEUS
- Poem by American about Yankee ship's hero
- Old Roman god guards unknown ship for hero
- Headless corpse has finally cut down children’s writer’s hero
- Doctor Seuss to underwrite non- standard parody of a legendary traveller
- Old Latin god saved unknown vessel for Greek traveller
- Legendary hero finding last of deadly doses concocted by us
- Revolutionary takes action against small party, harbouring yen to be epic hero
- Greek hero who had an epic journey to get home
- His Greek island tour became quite an epic
- Greek hero‘s trek cut short by us
Buddy explains!

The straight part
We know that "Greek hero" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greek hero = odysseus.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.