The Stygian Veil, commonly known as "veil", or abbreviated to just "v", is one of the four sections of DoA. Most of the enemies here drop Stygian Gemstones, although some drop Torments.
Veil's environment effect is called Demonic Miasma. This deals 50 damage to you every time you block or dodge an attack. To avoid taking the damage, it is often preferable to allow yourself to be hit by an attack instead of dodging or blocking it.
Shadow Form, Protective Bond, Protective Spirit, Shield of Absorption, and Dark Escape can all be used to reduce Demonic Miasma's damage. Lightbringer title does not reduce the damage, since it is not coming from a demonic servant of Abaddon.
A tiny area in the south-east of Veil is outside the effect area.
There are 5 hills to the south and east of the Dreadspawn Maw.
The south-west one, known as "ranger hill", contains a lot of Stygian mobs, including the ranger Underlord, and 2 Water Tormentors. The north-east one, known as "derv hill", also contains a lot of Stygian mobs, including the dervish Underlord, and many pop-up groups of Stygians and Torment Claws.
The three middle hills do not initially contain any enemies, but groups spawn on each hill during 360.
The Trench is a series of narrow passages leading all around Veil. It consists of the back trench, where all four Stygian Lords are found, and 5 smaller trenches radiating from the Dreadspawn Maw, one leading to each Lord, and one towards Gloom.
The 5 are known by the destination at the far end from the Maw, e.g. "monk trench" and "Gloom trench". Walking some distance down any of them will "pop the trench", causing a group of melee Stygians to spawn at each end of the trench and run to the far end, while 2 random Tormentors (always a Water, Soul, or Mind) spawn on the hills overlooking the trench.
The back trench stretches from the end of the Gloom trench all the way around to the Dreadspawn Maw, although the gate at the Maw is permanently closed. There are 11 groups, each consisting of Stygians and Tormentors, patrolling back and forth throughout the trench.
Breaching the Stygian Veil
Taking the first quest from the Adept of Whispers immediately opens the gates to the hills south-east of the Dreadspawn Maw, and a group of 5 enemies spawns on each of those hills. These groups run towards the Adept, and settle near him 33 seconds after spawning. Killing each of these groups spawns a new wave of 5 enemies on the same hill. The sixth wave on each hill is a mixed group of 6 enemies. These 6 waves are known as "360".
After all 6 waves of 360 have been killed, the gates to the south-west and north-east hills open. On the south-west hill, the ranger underlord spawns, together with Stygian Fiends, Stygian Brutes, and Stygian Horrors. There are also 10 Stygian Hungers on that hill, already spawned. On the north-east hill, the dervish underlord is already spawned. Most of the enemies on that hill are pop-up groups of mixed Stygians and Torment Claws, although there are also Stygians around the underlord. Killing both of the underlords completes the quest.
Taking the next quest from the Adept of Whispers opens the 5 gates leading into the trenches around the Dreadspawn Maw. The far west gate leads directly to the back trench, and does not open. The goal of this quest is simply to kill the 4 Stygian Lords.
Accepted the Brood Wars quest reward spawns 6 Smothering Tendrils around the Dreadspawn Maw. Killing each of these spawns a group of Stygians. Killing all 6 Stygian groups completes Veil, spawning the Stygian Chest and opening the gate to Gloom.