This is the complete list of heads for Axton in Borderlands 2 and how to get them:
Head Name: Roguish Renegade
How to get Axton Roguish Renegade head: Mission - In Memoriam
Head Name: Sandblaster
How to get Axton Sandblaster head: Drop - Badass Enemies
Head Name: Axton
How to get Axton Axton head: Default - Default Head
Head Name: Bone Blinder
How to get Axton Bone Blinder head: Drop - Vermivorous
Head Name: Special Edition:Snow Blind
How to get Axton Special Edition:Snow Blind head: Collector's - Collector's Edition
Head Name: The Hawk
How to get Axton The Hawk head: Mission - Statusque
Head Name: Medic Mantis
How to get Axton Medic Mantis head: Drop - Geary
Head Name: Mine But Not Yours
How to get Axton Mine But Not Yours head: Drop - Creepers in Caustic Caverns
Head Name: Space Knight
How to get Axton Space Knight head: Drop - BNK3R
Head Name: Grizzled Veteran
How to get Axton Grizzled Veteran head: Mission - Symbiosis
Head Name: Gallant Grunt
How to get Axton Gallant Grunt head: Challenge - Pay the Bills
Head Name: Radar Ranger
How to get Axton Radar Ranger head: Default - Default Head
Head Name: Handsome Jack's Mask
How to get Axton Handsome Jack's Mask head: Drop - Handsome Jack
Head Name: Wetworker
How to get Axton Wetworker head: Default - Default Head
Head Name: Vault Veteran: Lancer
How to get Axton Vault Veteran: Lancer head: Other - Completed Borderlands 1
Head Name: Dapper Gent
How to get Axton Dapper Gent head: Drop - Henry
Head Name: Shadaloo Stylish
How to get Axton Shadaloo Stylish head: Drop - Terramorphous
Head Name: Scurvy Dog (Pirate Head)
How to get Axton Scurvy Dog head: Buy Captain Scarlett and Her Pirate's Booty DLC