To start, if you have found your way here I am going to assume you have completed the Phantom Liberty story and Cyberpunk 2077 main story at least once. Seriously, if you have not, stop reading this solution and go do that first. While I am not going to outright give story plot spoilers I am going to give enough info that your first playthrough will be swayed rather than organic with you choosing.
If you're still here, let's get started.
There are 4 possible endings for Phantom Liberty with corresponding achievements.
King of Swords and King of Pentacles both put you on the path to obtain the mission "Things Done Changed" for The Tower achievement.
"But what do you I need to do to get the Swords or Pentacles endings?" you might be asking. Well, for one, the choice of who you betray during Firestarter does not matter. This is simply a choice of which confrontation you want to end with. Reed or Songbird. What is important is the final choices in the confrontation mission must end with both Song and Reed living.
Wording is going to get a bit tricky to try and not spoil things if you have completed one confrontation ending but not the other and more importantly not spoil this main story ending.
For King of Swords, call Reed while on the tram.
For King of Pentacles refuse Song's request while in the Core.
Basically all dialog choices must end with Meyers getting Song back alive and Reed offering you the cure. If done correctly Reed will tell you he will contact you after a few days. Wait or do other things in the meantime. Reed will contact you. Progress the dialog to tell him to pick you up on the roof above Misty's shop. This ending does not require you to meet Hanako at Embers to activate it. You can activate it at any time. It's a rather long ending. Enjoy.