Just to clarify, this isn't awarded from simply drinking the beer (
) three times in a contest, but downing three full mugs (which will require more than three drinks).
The beer refills faster as the game speed increases. If you drink early and tap too much, the game will move too slow to drink the 3 mugs worth.
Instead, let the game speed increase a good bit before drinking and don't tap too many times during the drink to slow too much. This will allow you to drink often and make it so your mugs keep getting refilled.