I modified LMEPHISTO's solution for the quick win method for all civs with the below modification to get this achievement.
AI Opponents: 5 or 6
Game Mode: Wonder Race
Map Style: Standard
Map Size: Small
AI Difficulty: Easiest
Game Speed: Normal
Reveal Map: All Visible
Starting Age: Post-Imperial Age
Screenshot of settings -
You may have to close game and restart until you see the 4 sheep near your town center
Once you have sheep and not other livestock, make one villager build 4-5 houses, set the two other villagers to build the wonder and then build additional villagers to continue the monument but the idea is not to win. Send scout and other villagers if needed out to snag the other sheep at all other civ locations. The other civs will only concentrate on building the wonder and will ignore the sheep. Once you have 20+ tagged for your civ send them back to the town center and once they are close the achievement will pop.