The Face of Extinction opens up with a cut-scene of Aloy speaking with Sun-King Avad. As they speak, the Eclipse are already making their way on to the Spire for a full on invasion.
After speaking to Avad, you're immediately faced with Helis and you must kill him. Close combat is probably your worst option here. Using your bows and traps are best for this boss fight. Timing when to explode the blaze containers will also help greatly and if you ever run out of running space, you can use the zip-line at the top of the second flight of stairs.
After killing Helis, take the zip-line down to the Ridge and help defend it.
A series of Deathbringers and Corrupted Machines will advance on the Ridge. Use the Oseram Cannon to suck up some bombs and launch them at the enemy. You will have to change positions every now and then to avoid the oncoming attacks.
As a finale to the defense, you will also have to deal with a Stormbird. You will have to drop your Oseram cannon and fight the Stormbird with your usually weapons. If you can get the Stormbird pinned down with a Shadow Ropecaster then you can pick up the Oseram Cannon again and fire at the Stormbird until it breaks free.
After defending the Ridge, Aloy will now have to stop HADES. Follow the Trail of Destruction and go to the Spire to stop HADES.
When you get to the Spire, HADES will summon a Deathbringer to protect him. Deal with the Deathbringer the same way you did with the previous one you fought. Take out its weapons first and target its weak spots when it deploys itself. Use the walls around the Spire to provide you some cover. This fight might be a little harder since HADES will occasionally summon Corrupted Machines to attack you. Tie them down with your Shadow Ropecaster if you have to keep them at bay.
Once you defeat the machines, use the Master Override on HADES and watch the epilogue of the game.
Congratulations! You've finished the Main Quest line of the game.
