This can be done in solo or co-op as the host or as a co-op partner.
There are two types of emoticon, ones post-game to express how one has performed, like "We Did it" or "$%#!@". The other type is in-game to indicate an action you are performing. e.g "Washing up" or "Serving". To perform an emoticon, press Y then choose one of the six actions using the control pad.
If you are playing Solo, you can choose either set to start tracking progress, but you must stick with that set to complete it.
If you are the Host of a co-op game, use the post-game emoticons to track progress to the achievement.
If you are a co-op partner, use the in-game emoticons, usually best right at the start so you're not rushed for time and having to concentrate on something else.
It appears that whichever set of emoticons you start tracking progress to, you must stick with that set in order to get the achievement.