Elex

I don't know if there are more people that you can have a relationship with in the game but I've unlocked this achievement having a relationship with one of the companions you find in the game, which is
The objective is having her to really like you, so my suggestion is to not travel with her. Otherwise, you may end up making a in-game choice or selecting a dialogue option that makes her like you less or makes her angry. You will know when this happens because the game notifies you.
So what I did was never travelling with her until I completed pretty much all missions related to her.

In fact, you will find the above mentioned companion for the first time in the Domed City and when she joins you, she'll also give you a mission.
She needs help investigating the Elex element and so you will need to escort her to different locations. Note that it may take several in-game days between one escort mission and the other. Visit her from time to time and she will tell you when she's ready to move on.
Once you have completed most of her missions she will idolize you (that's what the game says) and she will be ready for a relationship with you.
From now on, just travel with her until she will talk to you about your relationship. Choose the right answer (which will be pretty obvious) and, after a cutscene, the achievement will unlock.

If there are any mistakes (my first language obviously isn't English) or you have suggestions on how to make this guide better please leave a comment.

i was able to get Nasty and Caja to the point of a relationship in the same game, unfortunatly you then have to choose. They both advance with the main story and can be completed in Chapter 3, don't worry about factions or dragging them around, completing their companion quests and advancing the main story will have them as true Friends by Chapter 3, however Nasty's is a little more complicated and the more entertaining so ill start with her.

nastythe Dukes Sister lives in the Fort, you only talk to you once you have made a name for yourself in the Fort, adfter that you begin the quest. Nasty is a foul-mouthed violent angry bastard so she likes it when you talk to her in that manner. Angry Girlthis is a really tough quest I recommend waiting until you are mid--high level and have excellent ranged/heavy weapons. Get as far in this Quest as you can then visit the Cleric Stronghold the Hort and talk to Ulbricht, he's leading an offensive against the Abbs and wants you to find a suitable Commander, well Nasty is just the Girl.

The quest Ulbrichts Big Offensive will appear, go and talk to Nasty and she will agree and travel to the Hort. Make A Save before you begin, I highly recommend the weapon the REDEEMER which will make light work of themany Colossuss' you need to defeat.

After completing this Offensive, complete Chapter 1, I had Nasty based in Camp Origin so find her and she'll continue with the Angry Girl sidequest throwing you into challenging battles, again the REDEEMER is essential.

Complete Chapter 2

Chapter 3 - go find Nasty she will talk to you and open as as too why she finds these ridiculously hard battles, a quest line Salvationwill open up as well as Playing with Firethis is straightforward, gather the materials and brew the potion, then give the potion to Nasty, sleep 2 days and she will. She asks what you want from her, I said her assand she liked that. Then she asks if agree you have feelings and watch the cutscene.

Cajamuch simpler, complete her quest New Findings, each chapter you visit 2-3 locations, keep visiting her at her camp and she will tell you of Elex locations go and complete each location and she gradually likes you more and more, by Chapter 3 another quest will appear saying Caja has feelings for you, tell her you can imagine being with her, give her time to think and talk to her then watch the cutscene.