This achievement requires the help of another player or a 2nd controller as it cannot be done solo.
Four of the game's bosses guard princesses:
The Barbarian Boss in the Barbarian Boss level
The Cyclops in the Cyclops' Fortress
The Frost King in the Ice Castle
The Evil Wizard in the Final Level
In order to earn this achievement, you must defeat each of these bosses along with another player. You must then defeat the other player in order to kiss the princess. I did this in one session by replaying the appropriate levels with a friend (we actually did each level twice so we could both get the kisses). I believe that you could do it over multiple sessions as long as it's on the same character, but I'm not certain.
Per MathGuy42, you will not duel for the princess' kiss after defeating a boss if only one player is alive when the boss is defeated, so make sure two players are alive when the boss dies.