Dead Age

The best place to find Undead Cowboys is on Desert Night. Because Desert Night only unlocks around Day 35, the Undead Cowboy set of achievements will be one of the last "Kill" sets of achievement you will unlock, as the game ends on Day 42. You may have to farm the Desert Night a bit toward the end of the game to complete this set of kill achievements, since the opportunity to unlock them occurs late in the game (though you probably only need to make one or two extra trips to Desert Night to do so).

Only zombies labeled as "Undead Cowboy" or "Undead Cowgirl" count for this achievement.

Undead Cowboy Stats
Fast: No
Immune to K.O./Stun: Yes
High Defense (aka needs Breakthrough): Yes
Special Abilities: Take Aim (Debuff)
Priority Targeting Level (1 - 8, 1 is max, 8 is min): 6
Locations: Desert Night

Undead Cowgirl Stats
Fast: No
Immune to K.O./Stun: No
High Defense (aka needs Breakthrough): No
Special Abilities: Blind (Debuff), Molotov Cocktail (Fire DoT)
Priority Targeting Level (1 - 8, 1 is max, 8 is min): 8
Locations: Desert Night