Dead Age

The best place to find Undead Punks (not to be confused with living Punks, they're a different category of enemy) is in City Day/Night (after Area 11), though Undead Punks will also show up in Desert Night (again, after Area 11). Since City Day/Night, isn't available right at the start of the game (it opens up on Day 22), your best farming opportunity for Undead Punks occurs about halfway through the game, though you'll probably unlock these sets of achievements later than that due to the jump in difficulty for Areas 11+. You'll also always find a pair of Undead Punks protecting the City Day/Night boss in Area 20.

Only zombies labeled as "Undead Assassin" or "Undead Brawler" count for this achievement.

Undead Assassin Stats
Fast: No
Immune to K.O./Stun: No
High Defense (aka needs Breakthrough): Yes
Special Abilities: Adrenalin Push (Buff) Debilitating Strike (Debuff)
Priority Targeting Level (1 - 8, 1 is max, 8 is min): 8
Locations: City Day/Night (starting at Area 11), Desert Night (starting at Area 11), City Boss (Area 20)

Undead Brawler Stats
Fast: No
Immune to K.O./Stun: Yes
High Defense (aka needs Breakthrough): Yes
Special Abilities: Roundhouse Punch (AoE)
Priority Targeting Level (1 - 8, 1 is max, 8 is min): 6
Locations: City Day/Night (starting at Area 11), Desert Night (starting at Area 11), City Boss (Area 20)