I was able to do this with the default controller scheme, but 1 and 2 from other guides help if you have trouble using the default one. To aim you use
causes you to lean if you do so while aiming with
. To move while aiming, or as the achievement description reads, in iron sights, you need to aim while leaning, and also click and hold
down, which allows you to move. You need to hold
down to continue moving this way. Releasing it causes you to stop moving and lean if it's still tilted. Once you successfully kill an enemy while moving in iron sights in this way, you'll get the achievement.