Even after you learn how to beat Savathun on Legendary difficulty, the fight still takes some doing, so prepare for a lengthy encounter comparable to many dungeon bosses.
You fight Savathun several times during the finale of The Ritual mission. The first time you encounter her in an outdoor courtyard, you can safely plink away at her health while using the huts in the corners of the area for cover. The enemies that spawn in during this encounter, especially the three Hive Lightbearers right at the end, are generally more threatening than Savathun herself. Stay on top of the other mobs as you damage Savathun and she'll be 'dead' in no time.
Now it's time for phase two. Savathun will respawn and move to a distant island, and you'll find that she's much tankier this time. Once you deal a sliver of damage to her, she'll split into three clones around the ring of the arena. These clones are much easier to kill and they'll drop an aura on death. Walk through this aura to get the buff Glass Breaker. Once you get this buff, head to the portal in the middle of the arena, right in front of the big spire, and use the buff to disrupt the ritual. Repeat this process for all three clones and buffs to open the portal.
Once you're through the spire portal, you'll reach a new realm with several lit portals around the edge. There's a special Hive Wizard called a Threadweaver at the other end of each portal. Kill them to receive the Thread Cutter buff, which can stack up to three times. Once you've killed all three Threadweavers, you'll trigger a new interaction in the middle of the realm (which we won't spoil) and get teleported out.
With three stacks of Thread Cutter, you'll deal much more damage to Savathun. Once you shave off about 10% of her health bar, you'll be teleported back into the Threadweaver's realm with new portals available. Go through the portals to kill the Threadweavers on the other side, but plan on some Deepsight-aided climbing this time. Get three stacks of Thread Cutter and then return to the center of the realm to kill Savathun's three clones, not to mention the Thrall swarming the place.
Finally, we're at phase three. Savathun will summon what looks like a giant Ward of Dawn at this point, and the fight will become a revive-limited Darkness Zone, so be careful. Once again, we're going to need stacks of Thread Cutter to deal damage to Savathun. But this time, we're going to get them in the outdoor arena by killing the Threadweavers that spawn around the outer ring. Each Threadweaver is accompanied by a small group of Hive Acolytes, so take your time dismantling each group before moving to the next.
Once you get three stacks of Thread Cutter, the buff will get a 45-second timer. This is your DPS window. Push into Savathun's protective bubble and hit her with everything you've got – Supers, heavy weapons, grenades, Vorpal Weapon-equipped specials and primaries, anything. Savathun will hit you with her own Supers during this phase, so stick close to cover. If the Ogres and Acolytes in the courtyard become overwhelming, clear them out before focusing on Savathun. There's no rush here; you can run as many DPS cycles as you need.
When Thread Cutter drops off after 45 seconds, get out of the bubble and regroup to kill the next wave of Threadweavers. Repeat this process until Savathun finally falls. Nice work, Guardian.
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