Not so much a guide as some hints. The walkthrough here on TA is great and if you follow it you will pop this. But I replayed this game like 6 times so I noticed a pattern to maxing out their relationship. I'll be writing as if you were doing this on solo player mode, but the same principles apply on 2 player.
Despite this being a high percentage achievement it was one of my last ones to pop.
-At the beginning with Brand have him tell Alex to "Got with his gut" this way Alex will propose to Julia, when that happens say Yes as Julia.
-Try to always agree with Julia or Alex (you will play as both characters throughout the game) These will be a mix of Brain and Heart options. Do this by choosing encouraging options and romantic/playful options, as well as always help/ungag/rescue each other first.
-I'm not sure it matters if Julia decompresses or not, I had her wait and followed these other tips and it still popped. But if she comes up to quick don't have Alex stop her from drinking/tell her what to do. Again focus on encouraging and supporting each other. (This achievement will pop before the consequences of not decompressing occur.)
- I had Conrad escape the Duke when I got this achievement, so I'm not sure if he affects it or not. But if he is in your playthrough, as Alex, always side with Julia first or Conrad second. When they get separated from Conrad don't tell Julia to Shhhh either say nothing or shout for Conrad with her.
-When Julia gets spooked in the cafeteria say NOTHING as Alex, saying anything will get her to feel bad so say nothing.
-It seems a lot of times they max out their relationship in the Plunged chapter when they fall off the catwalk/bridge into the water have Julia tell Alex to stop. This is the moment when it pops for me as well as the moment it popped in the walkthrough here in TA.
-I don't think it is possible to pop this while trying to also achieve the Brain or Heart playthrough achievements, correct me if wrong!
As I said I played this game 6x through and noticed these tips as helpful. But I'm not gonna play it a 7th time just to make a play by play. 😅