There are many ideas for her already, but I’d like to add to the pool of Ideas so Blizz can pick and choose from a wide selection.
I want to design her around applying and exploiting poison damage.
May all who enter her presence feel her Anguish!
Trait (D): Anguish
Andariel increases damage per second done to all enemies in a medium radius around her that are affected by poison, If an enemy dies this way she gains health and mana. Anguish can also be activated to cause enemies in the radius to immediately take 1/2 of the total poison damage being dealt to them. 30 sec cooldown
Talents:
-Lvl 1 (Maiden’s presence): Each enemy hero hit by anguish lowers its cooldown by 3 seconds
-Lvl 13 (Suffering): Every 1 second an enemy stays within Anguish’s range and are affected by poison, Andariel gains mana and 10 armour. up to 50
-Lvl 16 (Seduction) When activating Anguish, the closest hero in the radius is stunned for 1 second
Q- Ability: Poison sting
Andariel fires a bolt of venomous energy in a line. passing through minions and applying dot but stops on the first hero hit, exploding in a small radius. The explosion deals little damage, but applies poison.
Talents:
-Lvl 1 (poison burst): Increases the radius of the poison explosion
-Lvl 4 (relentless anguish): Poison sting gains a second charge
-Lvl 13 (withering bolt): Poison sting lowers the physical armour of all heroes hit by 50.
-Lvl 16 (Unholy presence): Activate to fire an untalented poison bolt at the nearest enemy within anguishes radius. it also only deals 60% of the damage and applies half the poison.
W - ability: Noxious breath
Andariel sends fourth a wave of poison in a cone, dealing moderate damage, applying poison and slowing enemies (20%) caught in the fumes.
Talents:
-Lvl 7: (wall of poison): At the apex, the wave stands still for 1 second, dealing damage every 0.25 seconds. but not applying poison.
-Lvl 7: (Deep breath): Increases the cone range and width by 20% =
-lvl 7: (Vaporous travel): While the wave is travelling, Andariel can reactivate to appear in the middle of the wave.
-Lvl 16 (Draining wave): Gain spell armour for each hero hit with Noxious Breath
E- Ability: Whip of anguish
The Maiden of anguish lashes out with a magical whip of venom in a crescent the affected area widens from one point to another, it deals moderate initial damage and applies a moderate amount of poison.
Talents:
-Lvl 1 (Relentless punishment): Every hero hit with Whip of anguish lowers its cooldown by 0.5 seconds. Andariel gains 5% movement speed for each hero hit for 5 seconds, can stack.
-Lvi 13 (pain is pleasure): Each Hero hit with the whip gives Andariel 20 armour.
-Lvl 16 (Now, watch me whip!): Whip of anguish lashes a second time but the arc widens in the opposite direction for the second whip.
R1- Throne of anguish (a throwback to her throne room in D2)
Andariel sits upon her throne of Anguish, becoming immobile. Anguish has a much larger radius and now slows when activated, It applies poison every 0.75 seconds and it rapidly cools down. She may also use her Poison sting and Noxious breath whilst on her throne but only in a wide cone in front of her.
Talent:
-Lvl 20 (Guardian of the gate): Andariel can now use her ablities all around her and can teleport her throne once within her anguishes radius. she gains 50 physical armour and 20 spell armour while she is on her throne.
R2- Andariel’s Kiss
Andariel dashes forward in a straight line, latching onto the first hero hit and rooting them in the process. She bites then 3 time in 0.5sec intervals, dealing damage and healing each time for half. The third “kiss” applies moderate poison.
Talent:
-Lvl 20 (Lots of kisses): Andariel Bites down 2 additional times and the range of her dash increases by 20%. she gains Spell armor for each kiss
Other traits:
Lvl 1:(Manipulation): Andariel can bribe mercenaries.
Lvl 4: (Gate Keeper): Activate to lmbue a selected friendly structure with a levitating magical emerald that attacks nearby enemies. It deals little damage and applies a small amount of poison. Prioritizes heroes.
Lvl 20: (Emerald crown): Increases all poison Andariel applies by 15%. Her attacks become Ranged and burst in a small radius.
If you have ideas for more talents, feel free to comment them, and tell me what you think. 
. Id like some quest talent ideas even if you apply it to one of these talents it would be fine.