How to unlock the achievement.
As you progress through the story, at intervals, Noctis's companions will show up at Lestallum. The game clearly shows them arriving so it is not something you will overlook. Accept offers to train or skirmish with them. When you defeat the third and final companion, the achievement will unlock
Where to find the companions.
The three companions each go to the same location near the power plant. Just go all the way up the map to the power plant and turn left at the end. This is to the left of where you talked to Holly early in the DLC. Talk to each one and accept an offer to train or skirmish with them. This will initiate a one on one confrontation.Defeating the companions.
The tactics you use will depend on your game style and choice of weapons. I was efficiently going through the story and was resisting the temptation to be distracted by side missions. So, I was fairly low level and did not have any kick-ass weapons. It could be the game adjusts to your level and equipment. Nevertheless, it does not appear that any special preparations are in order. Gladiolus is first, then Prompto, and Ignis is last. The Gladiolus and Prompto fights are very straightforward. They could each be overcome by spamming warp attacks. (Note that there are no warp-out points so use a weapon that will permit multiple warp attacks if you want to spam warp attacks.) Ignis is more challenging. He has a 9,999 counter attack. He can be defeated with physical attacks; however, to do so, you need to employ precision blocking and dodge-rolls. I recommend magic attacks even though I rarely employed them in the rest of the DLC. For me, Ignis was weak to magic. The prompts for a magic attack are on the left. I was using a type C controller so a magic attack was
. I just spammed the magic attack & Ignis was unable to counter-attack.
The above tactics are suggestions. You will have preferred weapons and tactics based on your play style. Use them. The companions are not super bosses that require a specialized approach. Use what you are comfortable with. This comment applies to the below note as well. You have a lot of flexibility. There is no 'right' set-up. The game is designed for you to have fun. Set up your protagonist according to your personal tastes and play according to your favorite play style. A note on birthplace - not directly related to unlocking the achievement but may affect your choice of tactics.
The tactics I outline above - warp attacks against Gladiolus and Prompto and magic attacks against Ignis - may be dependent the birthplace you choose at the beginning. I chose Galahd - offensive specialist - high power & magic. This is what I recommend for the entire DLC. Per, the disclaimer above, this is just a suggestion and I do not mean to dogmatically imply that there is a 'best' birthplace. The other birthplaces have advantages in HP, MP, vitality, & spirit. Nevertheless, the tactics you use throughout the DLC can ensure that you are not dependent on any of those. So, I recommend getting the highest power and magic you can and use them to kick ass. In most instances, you can use warp attack, warp out tactics so you're not taking hits, your HP stays high. Moreover, your MP regenerates when you warp out.