In order to get this achievement you need to play any combination of the 6 fun games 10 times, as Inbred Friend states.
Rodeo is indeed the quickest, but not not necessarily the easiest game to complete the criteria. For example, I found the Race with Katelyn to be the easiest (and approximately 45 seconds +/- to complete).
Additionally, I wanted to clarify you can play the same fun game 10 times to earn this achievement. You do not have to play all game types for this achievement, and it will pop immediately after your 10th game completion.