All four players should go into the Pack-a-Punch room, and four Keepers should be near the Gateworm pedestals.
Interact with each of them, and then the boss fight will begin. The Shadowman will appear, and when he has a circular aura around him he cannot be damaged. But when it disappears, all players should begin shooting him with their automatic weapons, and continue to do so as he teleports around the room. With enough damage in a short amount of time, he will teleport closer and closer to the ritual altar.
Once he is above it, a player will need to interact with the altar to pull the Shadowman into the Summoning Key, defeating him. If you fail to damage him enough in a short amount of time, interact with each Keeper to get rid of his aura and try again.