The beer and sausage contest is a minigame early in the game. The characters will refer to it so you will know it will happen. I suggest doing this on easy.
On the side of your character buttons will fall from the top of the screen. When a button arrives on the designated area of the bottom of the screen you have to press it. The more you hit the faster the buttons will come down. There is a giant bar between your character and the falling buttons. The more buttons you hit the more this fills up giving you a general idea of the speed. The following buttons can fall







.
In front of your character there is a beer mug. Eventually you will be able to drink from this with

. This slows down the falling buttons more and more as you repeatedly press the

after taking it in your hand. The giant bar empties accordingly. The more you drink the slower the buttons become and the less beer you can drink. For this achievement you want to do the opposite.
To drink enough beer:
1, hit as many buttons as you can
2, drink as soon as you can but only press

ONCE (to put it to your mouth)
3, do this until the giant bar is halfway
4, after the bar is halfway keep it just below it (3 sips /

s every time)
5, hit the buttons until it gets to halfway again then drink 3 sips again
6, you should get the achievement with 30 seconds left