Tier 4 - Masters of the World
Fingolfin (Tolkien)
Ecthelion (Tolkien)
Gil-Galad (Tolkien)
Glorfindel (Tolkien)
John Carter, Warlord of Barsoom (Burroughs)
Icarium (Erikson)
Tier 3 - Masters of the Realm
Hurin (Tolkien)
Conan (Howard)
Corwin of Amber (Zelazny)
Aragorn (Tolkien)
Drizzt Do'Urden (Salvatore)
Mandorallen (Eddings)
Tier 2 - Heroes of the Realm
Morley Dotes (Cook)
Paksenarrion Dorthansdotter (Moon)
Aillas of Troicinet (Vance)
Legolas (Tolkien)
Gimli (Tolkien)
Brienne of Tarth (Martin)
Bard (Tolkien) - Bumped up one place to Hero of the Realm tier
Fafhrd (Leiber)
Tier 1 - Local Heroes
Eomer (Tolkien)
Eowyn (Tolkien)
Cugel the Clever (Vance)
Merry (Tolkien)
Samwise the Brave (Tolkien)
Icarium has depopulated multiple cities singlehandedly, and is repeatedly afflicted with amnesia by the gods because they're afraid of what he'll do if he remembers what he is. Now that's an epic-tier fighter.
Meanwhile, Fafhrd is strong, skilled, and mostly fearless, but he's not particularly ambitious, so I'd put him a tier lower than Conan.
Moved Cugel down one because I can't remember a time he actually fights, as opposed to running away or using trickery. No way he would ever have faced the Witch King, for instance.