Sudden Death occurs when either both fighters are knocked out simultaneously or time runs out with both players having the same life left. You'll want to go for the latter method as it's much easier. In this round, two or three hits will knock out the other fighter so be careful.
Unfortunately this achievement cannot be unlocked using a second controller, but it's still not all that difficult. Go into the game settings and change the Difficulty Level to Easy and the Round Time to 30 seconds then start Original Mode > Arcade. The strategy is to just avoid your opponent for the duration of the fight. Constantly move away, and if they do manage to get up close just guard and let them attack once before moving away again. Two characters you might want to try with:
Taki. She's the fastest character and you can leap forward a fair distance with .
Yoshimitsu. He's also quite fast and can actually regenerate a small amount of health with if you do manage to get hit.
Alternatively you can do this online. Besides extreme luck, boosting is pretty much the only way this will happen, so look here for boosters.