To start the main quest you must turn on the power and get to the sewers.
You will need to grab a panel next to the Pack-A-Punch and place it next to the monitors in Test Environment.
Now interact with the monitors and a cutscene will start.
After the cutscene ends you can now open the hatch on the floor and take the Ghost A.I. from Destiny.
You will have to achieve 4 challenges to power on the 4 monitors. Those challenges can be done simultaneously, and I really recommend doing it since most of those requires you to pass round.
To get the green screen turned on, you need to play Sharpshooter at 5 locations.
To start this step, you need to stand on the target at Twin Bridges, then a target will spawn around you, shoot it and another will spawn.
You need to stay inside the circle, if you make a step outside, the targets will disappear, and you will have to try again. Once done, you will have to wait till next round for the next Sharpshooter circle to spawn.
5 : Spawn Area
Once done, Tyrant will tell you that the green terminal is active.
To get the yellow screen turned on, you need to turn on and protect 3 generators.
Once you turn on one, a horde of poisoned zombies will spawn while the generator is charging.
Kill them before they destroy the generator, or you will have to try again next round. There is no particular order to do them, but you can do only one per round.
Once done, Tyrant will tell you that the yellow terminal is active.
To get the red screen turned on, you need to find 3 fuses by doing particular steps and input them in front of the power switch.
There is no particular order to get the fuses, but you can only carry one at a time.
One of the fuse can be obtained by shooting the red pustule in the Sewers with a Pack-A-Punched weapon.
One of the fuse can be obtained by killing a Big Soldier Boi after you got the Tyrant cutscene at the beginning of the quest.
For this fuse you need to get 2 items from the trader pod : the Tear Gas Shield and the Hydraulic Tazers.
Now get to the Police Station garage, you will see a red light coming from behind the wooden planks.
You first need to melee the planks with your shield, and then you need to melee the fuse with the Hydraulic Tazers in order to charge it up.
Once all fuses are input into the monitor, Tyrant will tell you that the red terminal is active.
To get the blue screen turned on, you need to follow a blue orb and fill it with souls every time it stops.
This step is pretty hard as the orb will stop at some pretty tricky spots, gather every thing that can helps you (Attractor Axes, Murder volt...) Pack-A-Punched starting pistol with PhD is pretty good for this step.
First you need to interact with the generator, in Test Environment, in front of the terminals.
Here are the 4 stops of the blue orb :
Main Road
Water Refinery
Police Station, first floor
Sewers
Once done, interact with the generator once again and Tyrant will tell you that the Blue terminal is active.
Once all 4 terminals are actives, come back to Test Environment and interact with the terminals.
Another cutscene will start, after that you can take Tyrant's phone.
Go the the Sewers and put Tyrant in the computers, another cutscene will start and you can take back Tyrant after it ends.
Go back to Test Environment, interact with the terminals once again, one last cutscene will start and by the end of it, you'll get unlimited perk slots.
To start the boss fight, come back to the spawn area.
From now on I greatly recommend :
Getting mule kick
Getting rid of the Murder Volt since it doesn't do any damages to the boss
Getting the Rat King
Getting the Shadow Cider perk
Interact with the distress rocket, and the boss fight will start.
Now you need to survive until the floor gets electrified, at this point, get on the platform and shoot the boss.
Once you get to the second phase, you can shoot him almost at any time (as long as you got hitmarkers, you're good).
After you killed the boss, congratulation you've beaten Rainy Death, you can now enjoy the ending cutscene with a wholesome message from HitmanVere, the creator of the map.