Start a round and do not get any words. When you finish your score will be zero. You will see a leaderboard screen after the round ends. Tap one or two people's names that are around you. Then the next game, actually get a score above zero. When the round is over you will unlock the achievement.
If you have a friend who has played the game in the past 24 hours, you can simply pass their score without adding any "Frenemies."
This is what the "Frenemie" page looks like. When selected, their names are a lighter color than the background.