You'll want to use a diamond sword for this. You can beef it up with enchants like Smite or Sharpness, or you can just drink a Strength II potion. Unless you're lucky with enchanting and have XP to spend, making a potion is easier.
To make a Strength II potion, make a Strength I potion (nether wart, then blaze powder), and then add glowstone to increase it to Strength II. Drink the potion right before you find your target, the potion only lasts 1:30.
To get the last bit of extra damage, you'll want to do a critical hit when fighting whatever it is your want to kill. To do this, jump off of something or simply jump in the air, and swing while falling back down. You'll know if you get a critical hit by the white sparks/stars that pop up.
I think the critical hit damage is random, but most of the time you will one-hit-kill the enemy.