The Bossfight is divided in five stages
When starting the fight, you will spawn underwater and need to swim to a nearby tree. Here you will find the Sentinel Artifact, interact with it to be teleported back to the Titanic. Once on the ship, a giant iceberg will appear, along with a giant blue eye. Shoot at it but mind you that no actual damage will be done to the eye (so don't waste your most powerful weapons. Shoot it until you are teleported to the stairs behind. Now you must survive a large assault of zombies, Stokers, Catalysts and Blightfathers. If you survive and killed them all, you will proceed to the next stage.
You will get teleported to the Engine Room and need to survive another intense wave of enemies. No need to shoot the eye, as bullets still don't damage it. Just kill the enemies and try to stay alive.
You will get now get teleported to the State Rooms. An even more intense wave of zombies will begin, additional to the Eye being able to damage you using its beam. However, this time you can also damage the eye, but only when it shoots its beam. Once you damaged it enough, you will be teleported to Stage Four.
You are now on the side of the ship. Do the same as last step, and damage the eye enough to proceed. Stay out of the circles!
The final stage. You must now kill the Eye, while also slaying large hordes of the undead. Dodge the attacks of the Eye. Once you destroyed it, you have completed the Easter Egg.