This continues directly from The Lesson, as you go after Faith once and for all.
You can't avoid going through the gate, so don't try. Instead let the Bliss lead you to a brief convo with the Sheriff, and then a relatively cliche but awfully forgiving boss fight with Faith.
For the early part of the fight, when Faith appears, shoot her. As the fight wears on, duplicate Faiths and Angels will appear (but no Buffies). The duplicates and the Angels only take a single bullet to dispel, though the latter can hurt you if they get in melee range. Just keep popping illusions until you find the real Faith, and do as much damage as you can before she disappears.
The biggest threat here is the energy barrage Faith tosses at you, but even these bolts can be dodged fairly easily. Just don't plant your feet when you fire- keep moving. Note that, in the center of the stage, medkits and ammo crates are constantly appearing to replenish your supplies.
This cycle continues until you finish her off. She'll hurl a few cryptic hints at you and expire, leading you directly into the Walk The Path mission.