The HAM Archer is only fought during the Another Slice of H.A.M..
During the quest, when Zanik is telling the goblins of the Goblin Village to abandon their violent ways, H.A.M. attempts to assassinate many of the goblins in the village. The ambush consists of two H.A.M. members, the HAM Archer and the H.A.M. Mage.
The archer manages to snipe at least one goblin, and must then be fought by the player by sneaking behind several buildings and climbing onto the watchtower where the snipers are hiding. The archer and mage hide behind a row of crates and boxes, and so can only be hit with ranged or magic attacks. There is a bronze crossbow and fifty Bronze bolts nearby, which can be used if the player did not bring an appropriate weapon.
The HAM Archer's method of firing his bow is unique, and is much smoother than normal players'. He also uses arrows with pink feathers, which cannot be obtained by players and are not currently used by any other NPC.