On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Bad Hair Day. This is one of the several side missions that you can unlock during the exploration of the Southern Shelf location.
1) Monglets lair
2) Monglets lair
3) Monglets lair
4) Monglets lair
Go behind the Bandit camp in the south  (after destroying the electric fence), where you will find a Monglets lair. There are three additional places marked on the map where you can complete this mission. You have to weaken the Bullymong by its health to 10-15%. When the enemy starts crawling, finish it off with a melee attack (by default V). That way it will drop a Bullymong Fur which you have to pick up. Repeat this four more times and return to Hammerlock  or Claptrap (different prize) to complete the mission.