This one is annoying and luck based. Basically, your odds are better the more players you have, so I suggest starting up a game with 8 players. From there, you can idle until the final round (the one with the pictures), but it does expedite the process if you just click random things instead of letting the timer count down.
Once you get to the final round, pay close attention to the choices given to each player. Everybody is given 2 to choose from, and you're looking to select the one that says "A moose."
At this point, you've earned the achievement, but I forget if it pops immediately or if it doesn't show up until the actual picture of the moose is shown on screen. If someone could confirm either way, I'll tweak this bottom part! Either way, you need to select "A moose" and the achievement is yours!