This will probably be the first achievement you get in this game, but depending on your play style it may take a couple fights.
Without spoiling 1-1/1-2, Kirito and Eugeio are out in the fields along Ruild and have a few low level, generic monsters you have to fight through. So here's how you get the achievement.
Make sure that you are playing as Kirito, weaken a few enemies, press and hold R1, then hit either 🟧 or 🔺 (Has to be Kirito because Eugeio won't have any skills yet since it's basically a tutorial), and hope the hit you make off of that combination is the killing blow to one of the enemies.
Personally I've had much success with the first skill Kirito unlocks getting kills, that'd be 🔴 on the keypad. But any of the skills will work.
Im going to try and fill out the True Achievement page for this game as well, as I'm playing on the PS4 but the conditions are identical. So be on the lookout for more from me in the coming days. And don't forget: Sinon best girl. ;)