First off, I want to make this completely clear. You can NOT crit the fingers at either North or South hills, and they do NOT take condition damage.
Your gear should depend largely on your class, the same as with every other spot on this boss, excluding the zerg which uses Soldier's gear, Cleric's, or Dire, depending on your class. Though Dire is largely useless at both Hills. I recommend using either Soldier's or Cleric's, depending on your class.
The main focus at both North and South Hills, NH and SH, is to eliminate Tequatl's Fingers that spawn, and to protect the turrets from the mobs that spawn there as well. Focus should remain on the Fingers mostly, however, as 1-2 people can easily pull the mobs and keep them away from the turrets on their respective sides.
Priority: Fingers closest the the turrets first, mobs, remaining fingers. This is true for both North and South Hills teams. It is also crucial for the North team to clear the North Beaches of fingers and mobs before heading to battery phases, as well as South doing the same for their side.
Being able to hill is also a large help, as you will take a large amount of damage from the AoE poison ring that the Fingers cause if the turrets are lacking in being able to cleanse properly.