Select 'Fatality Tutorial' from the Training menu. Pick a character and then complete the fatality as instructed. Select Infinite Timer so you have unlimited amount of time to practice the fatality and remember to stay inside the green box.
Easiest to do this with Scorpion. Go up close to your opponent as soon as you hear the 'Finish Him!' and press . Watch the button meter at the top to see if you are pressing the right combination. The screen should then turn black, the fatality is performed, and achievement unlocked.