To do this, you must first be in a romance with a character. You do this by choosing the heart dialogue options, talking to the companion, giving gifts, and getting their friendship rating to the maximum.
At the end of the game, there will be a time when you will get a chance to talk to all your party members. When this happens speak to your love interest and simply choose the "I love you" dialogue option. This will "complete" the romance; therefore, unlocking this acheivment.