I suck with the sword and hardly ever pick it up but I eventually got the achievement on my old account just by being in the right place at the right time.
I wouldn't recommend just picking up a sword and running around thinking "Steppin Razor, Steppin Razor". You can't get a triple kill if there aren't 3 people together. While you're in a game try to figure out where battles are happening and then linger around there (but out of harms way) and try get 3 in a row who don't see it coming.