Ok, so I've tried to file it down to this version of the Ranger Legendary-Path Transmute with everyone's input in mind. And I've included some concept art for the Relic and Legendary (all images shamelessly stolen and altered from the web).
UR - Amulet of the Agile Shot - Neck - Any
+2 Dex, +2 Ranged Damage
(Or)
UR - Bracers of Supreme Archery - Wrist - Any
+2 Ranged Damage +2 To Hit to all ranged attacks and +2 Damage to all ranged attacks made with physical weapons.
Relic - Amulet of the Sharpshooter - Neck - Ranger
+3 DEX, +5 to favored damage; add favored enemies (Giants, Fea, and Constructs)
Legendary - Heartseeker (or Taulmaril) - Neck - Ranger
+4 to DEX, +7 to favored damage; ignore damage reduction/ crit block of favored enemies,
add favored enemies (Giants, Fea, Constructs, Dragons, Evil Outsiders, and Aberrations)
Little bit of D&D History: Taulmaril, also known as the Heartseeker, was Catti-brie's magic bow, which passed on to Drizzt after her death.*
*R.A. Salvatore (March 2014). Night of the Hunter