The ending requires you to accompany Phineas and help him on a mission. Your task here is to meet his contact in Monarch. You then have to get some Dimethyl Sulfoxide among other stuff you have to collect. Phineas intends to take down the Board and will take you straight to Tartarus.
This ending will require you to fight all the soldiers of the Board and then finally confronting the Chairman Rockwell. At this point, there are two paths you can take. You can either convince Chairman Rockwell to be on your side, or fight a giant robot.
If you fail to convince Chairman Rockwell, you will have to fight a giant robot boss, followed by talking to Sophia Akande. At this point, there are two paths you can take. You can either kill Sophia and loot the key off from her to free Phineas, or you can persuade her to flee and not face the consequences.
Your persuasion will only work if your skills are high enough. Your Intimidate should be above 85, and your Persuade should be at 100. This along with your Heavy Weapons should be at least 55, and two-handed melee weapons should be at 85. You can then Intimidate her and try to persuade her to run away or she will be killed by you.
Once you are done with everything, go and talk to Phineas and he will give you a glimmer of hope by populating a new home in Halycon. There, you can rebuild your colony and revive The Hope.