As you play the game, you'll be awarded "Dating Tokens" after each round. More gaming tokens lets you date other hen. There are only three hen total, requiring 0, 50, and 200 dating tokens. It's basically just unlocking higher difficulties. But higher difficulties equals higher rewards as well.
So just try to get a lot of combos, and keep a game as long as you can. Move to the next hen as soon as you can. And then just grind until you've got 2000 dating tokens(amount only visible in the dating menu). The achievement unlocks once you end the game that gave you dating tokens to surpass 2000.
It took me roughly 90 minutes in total.