Will of Crota/Walkthrough
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Head inside the Terrestrial Complex. There will be multiple Fallen waiting around the edges of the room, including a few snipers and melee Captains. Stay close to the room entrance to minimize enemy avenues of attack, especially when the melee Captains, Stealth Vandals, and Shanks rush in. After some enemies have been defeated, a large number of Hive will start entering the room, mostly Thralls. Defeat the Thralls quickly, as there will still be Fallen and a few Knights to contend with.
Once the room is clear, a few more Fallen will come down the stairs on the opposite end of the room. Dispatch them, and head upstairs to the next area.
Objective: Kill Physkin, King Baron
The room upstairs is empty, but immediately outside are numerous fallen, including more snipers and melee captains. Fallen reinforcements will start arriving via Skiffs near the edge of the cliff, so maintain distance and pick off enemies before they get close to the doorway. Be aware that there is one sniper camped out directly above the doorway, so take him out before venturing outside. Also be wary that walking a few feet outside puts you in range of the Skiff's guns, so find good cover. The last wave will deploy several captains, including Physkin, King Baron. Eliminating him will allow Guardians to venture to the next area.
Guardians will enter the Skywatch public area. This area can be skipped entirely, but entering it triggers a Tombship to appear, deploying a Hive Knight called Protector of the Will. He can be ignored.
Enter the Jovian Complex and have Ghost open the door. Inside, Omnigul is waiting; she summons a swarm of Thralls and some melee Knights with a few cursed Thralls mixed in. Two Wizards will also appear at the end of the hallway. Kill these Wizards before turning around the corner, as a lot of enemies are waiting on the other side. Omnigul will start summoning more cursed Thralls and an Ogre. There are also several Sword and Boomer Knights at the top of the incline, so be careful not to rush and thin out the enemy defenses.
Objective: Kill Omnigul
At the top of the incline, the fireteam will reach another small room opening into a larger room. Inside this larger room is Omnigul, who will remain mostly on top of a catwalk. She is surrounded by Acolytes and Boomer Knights, but will also summon Sword Knights, Thralls, and Cursed Thralls every time she loses 20-25% of her health. Thin out the enemies before engaging Omnigul, as she is very difficult to deal with if there are other enemies nearby. Retreat every time she summons more enemies; if needed, there is a ledge in the previous room that enemies can't reach, making it useful for avoiding Thralls and Knights (Cursed Thrall explosions may reach you though). During the later part of the fight, Omnigul will also summon Wizards, which will flank her and fire very rapidly and throw down poison. Remember that Omnigul's shields are Arc, not Solar, so equip appropriate weapons.
While the small entry room is relatively safe, an alternate strategy requires the full fireteam to rush to a nearby ledge at the opposite end of the room. This room has very limited cover (only enough for one Guardian) so the other two are exposed. However, the Guardian behind cover can revive the other two, allowing them to try to burn through Omnigul's health quickly.
Next to the entry room's entrance there is a small ledge that a single Guardian can use to attack Omnigul. It is very exposed with limited cover. so take care to avoid drawing undue attention. Be warned that a Sword Knight spawns occasionally on the ledge to flush you out.