This is achieved by losing all your lives in Arcade Mode, and then selecting "Yes" when asked to continue.
Start a game in Arcade Mode, choose 10-mile Gorge, lift your left hand when prompted to start the round, then wait for six minutes. If you physically leave the view of the Kinect, the clock will stop at when you left, so, unfortunately, you have to hang out for six minutes while the timer counts down for the round. Coming in last will cost you one life.
Do the boat race as normal; you can't lose a life in the boat races.
When the second fishing area comes up, do the same as before. When you come in last again, you will lose your second (and last) life, and will be prompted with a countdown timer to continue. Choosing "Yes" will net you this achievement. Choosing "No" or letting the timer expire will net you the "Don't give up!" achievement.