Load up rally point Bravo on Tip of the Spear normal or higher. Cross the bridge and into the structure.
Near the top of the first set of stairs you should see several Covenant along the walkways ahead. Hang back on or near this first staircase and clear them all as much as you can before proceeding forward. At the top of the next set of stairs do the same, and grab a Needle Rifle from the Covenant weapon box to the right and be sure to conserve some ammo for it for just a moment.
Watch out for a turret around the next corner with an Elite and a few other enemies milling about. Around the next corner a set of stairs leads down to a walkway that ends abruptly. DO NOT drop off of it into the courtyard below. When you go down these stairs, a red V-shaped enemy marker will appear on the roof of the building across from you. This is the Elite Zealot. Quickly kill him with the Needle Rifle to unlock ‘Your Heresy Will Stay Your Feet’.