You need a hug gesture from three (3) different people in online co-op. You earn the hug gesture after Course 03; Hard-Light Surfaces.
You can hug in any area during the course including the main Central Hub and it will count towards your three hugs. Once you finish the hug you can quit the session; no need to jump into a course or complete any tests.
You can hug someone who hasn't completed Course 03 and both players will count for the achievement. Hugs are shared so you don't need to perform two hugs to count, one will record for both players.
You must be friends with your partner prior to the game for the hug to count. Friending them in-game and then hugging them doesn't count. You can friend them in-game, leave and then start a new session with the player who is now your friend and it will count.
Split-screen doesn't count, even if you do split screen on the same console and each person is on a separate Xbox Live gold account. You will need to be online using separate consoles.
Unlocking this achievement also unlocks an avatar award; a gray "Love Shirt" with an image of both robots (Atlas and Peabody) hugging. The image is similar to the "Friends List With Benefits" achievement icon image, but in color.