This achievement is story related and can't be missed. However, here are a few tips to make this achievement easier.
First, an Outsider is a crystal alien that when first met, is a glowing pink/orange/reddish crystal and then it morphs into a humanoid during it's cutscene. These aliens are only found on spaceships that either crash landed or set down. I have never seen them in any other missions, only ones where you fight in and around spaceships.
Second, these guys only have 3 health bars, so almost every weapon will kill them in one hit. Because of this, DO NOT OVERWATCH! You don't want the creature moving and then getting shot down while you are trying to manuever your arcthrower soldier into range.
Thirdly, if you can, shoot them once with an unmodified pistol. It only does up to 2 damage, so won't kill the Outsider and it's reduced health will make the stun attempt easier (The stun starts out at a 70% chance if the enemy has 3 health, 80% if they have 2 health, and 90% if they have 1 health). Yes, I have missed a stun at 90% once or twice, so that leads to my next tip.
Fourth, SAVE BEFORE YOU MOVE INTO STUN RANGE. If you fail that crucial first stun, you will be right next to the alien and get shot in the face. This is not fun. So save your game BEFORE you move into range, and that way, if you fail the stun, you can reload and try again. There are rumors that the hit probabilities are set at the beginning of every turn, so if you miss and reload, you will always miss until you forward to the next combat turn. I've not tested this personally yet, but if you save before you move, there is no risk of this rumor becoming your problem.
Please either comment below or send me a Personal Message if you have any comments or improvements.