Adapted from a clone of Valkyn's Enslavement by magnusthorek, in this library, and from Devil Jason at http://esoacademy.com/builds/pve-magicka-sorcerer-dps-build-by-devil-jas0n/

For solo questing, you may want to add a Familiar or Winged Twilight for some tanking and healing.

Devil Jason shows the following skills by bar:
Bar 1: Hardened Ward, Bound Aegis, Crystal Fragments, Force Pulse, Inner Light, Shooting Star
Bar 2: Streak, Bound Aegis, Power Surge, Liquid Lightning, Inner Light, Energy Overload
Bar 3: Mage's Wraith*, Hardened Ward, Dark Conversion, Bound Aegis, Inner Light

*Use Endless Fury, the alternate morph, specified in magnusthorek's build.

DPS bar, adapted from Zion:
Shattering Prison (fr Encase), Lightning Flood, Elemental Blockade, Structured Entropy (or Hardened Ward), Inner Light
Zion says do the following:
1. Aggro to get the mobs together
2. Structured Entropy
3. Shattering Prison
4. Lightning Flood
5. Elemental Blockade
6. Use staff to finish off any strays

Devil Jason says:
GEAR AND ITEM SET INFO
Elemental Succession Set: 2x Rings, 1x Necklace, 2x Clothes (NOT hat or shoulders)
Molag Kena Set: 1x Helmet, 1x Shoulders
Law of Julianos Set: 3x Clothes (The remaining pieces)
Bar 1: Julianos Inferno staff
Bar 2: 2x Julianos 1H swords
Try having every armor piece with divines trait and every weapon with precise.
About the Enchantments: 3x Jewelry Spell Damage 5x Max Magicka 2x Max Health (1 for Chest and 1 for Gloves) 3x Weapon Shock Damage
The basic build must include 5 pieces of light armor, 1 piece heavy and 1 medium so the undaughted guild passive is maximized. To achieve that you can alternatively craft some of the Julianos' pieces heavy or medium.

CHAMPION POINT TIPS
Warrior Points: Max Bastion ,then all in Elemental Defender Thief Points: Magician (Alternative: split between Magician and Arcanist) Mage Points: Elemental Expert (Alternative: split between Elemental Expert and Thraumaturge)

GENERAL INFO
Because of the Energy Overload Ultimate, there is a 3rd Ability Bar.The Abilities are: 1. Mage's Wraith 2. Hardened Ward 3. Dark Conversion 4. Bound Aegis 5. Inner Light

Attributes: Magicka:64 Health:0 Stamina:0

Mundus Stone: The Apprentice (Alternative:The Mage)

Food: Any Vr15 double-stat Magicka-Health is good (I use Melon-Baked Parmesan Pork) Play Style: Flame-Force Pulse
Motive: The most important thing about this play style is this motive. The way it goes is: Starting with a medium destruction staff attack (= by pressing the attack button slightly more than a light attack just so two fireballs come out), then immediately force pulse, after that a medium destro staff attack and so on.

Actual Play Style:
Starting with Bar 2 activate Power Surge for buff and self healing. (Of course Bound Aegis and Inner Light must be already activated as they are toggle on abilities).

After that, activate Daedric Minefield (If you choose it over Streak) and Liquid Lightning, and place them where mobs will be, and bring them there as soon as possible.

To bring them there use 2 light attacks from the fire staff when fire signal from Elemental Succession appears, in order to proc both its passive and Molag Kena's Set passive.

After that comes the main damage which is the Flame-Force Pulse Motive, but each and every time Crystal Fragment procs, you have to activate it, between the Motive.

The activation of the Hardened Ward depends on the enemy you are fighting.
If it is an enemy that will instantly kill you without a shield, activate it right after Power Surge.
And if it is a simple enemy, or group of simple enemies, you can activate it right after Daedric Minefield and Liquid Lightning.

When the enemy comes down to 20% Health or less, activate Energy Overload and spam Mage's Wraith to execute.

When low on Magicka, use Dark Conversion and Energy Overload light or heavy attacks to restore Magicka.

In case you want to nuke enemies, use Energy Overload (light attacks for single enemies or heavy attacks for group of enemies), or if you need damage and Crowd Control, use Shooting Star in combination with Liquid Lightning where the meteor fire is.

My Play Style: (There are small differences with the previous one)
First of all I prefer Streak over Daedric Minefield, because I like to damage and stun, or mainly avoid enemies and their attacks (mostly bosses that insta-kill you).

Use Hardened Ward right after Power Surge at all times.
Then use Liquid Lightning when mobs are chasing and place it where I will keep them until it ends while I use Flame-Force Pulse-Crystal Fragment Motive.

For max DPS, I use Power Surge, Hardened Ward, Liquid Lightning and Energy Overload (light or heavy attacks depending on the situation), or Shooting Star with Liquid Lightning combo while using the Motive.

If low on Magicka, I combine Dark Conversion with Energy Overload attacks and if ultimate runs out, I use Dark Conversion only.

General Tips:
1. As long as you have Magicka, you can use Hardened Ward to stay alive, so without Magicka you're basically dead. Ways to restore Magicka: Energy Overload, Dark Conversion, fully charged destro staff attack.

2. Be sure to have more than 10-15% Magicka in case you need a life-saving Hardened Ward.

3. While in a fight, be sure to buff yourself again if needed, but if not, it's not the end of the world. (It's more important while in execution phase) Also if possible proc the two sets passives again in the fight.

4. Of most importance is the right use of Hardened Ward. Use it when the previous damage shield is over or nearly over. Avoid spamming it unless needed!

5. Don't spam Streak unless it's ABSOLUTELY NEEDED, because Magicka will be massively consumed.

magnusthorek says:
For end game:
Equipment
- 5 Law of Julianos (light)
- Valkyn Skoria Set
- 2 Nirnhoned Inferno Staff (main-hand)
- 2 Nirnhoned Swords of Torug's Pact (off-hand)
- 3 Willpower Jewelries with Arcane trait

* All upgraded to Legendary state

Notes

- As pure DPS build for PvE, all pieces of gear go with Divines trait, including the Valkyn Set if possible all enchanted with Legendary Truly Super Glyphs of Magicka for larger magicka pool.

- For one of the Destruction Staves the main option is a Glyph of Poison since it applies the long lasting Poisoned status effect as well as the explicitly mentioned Poison damage.

Another option is a Glyph of Flame for even more flame DoT and even more chances to proc Valkyn's meteor

For the second staff we have a Legendary Truly Superb Glyph of Prismatic OnSlaught made with a Hakeijo specifically designed for places crawling with daedra / undead (WGT, ICP, Imperial Sewers...)

- For Jewelries there a Legendary Truly Superb Glyph of Increase Magical Harm is your best bet for even more Spell Power but a Legendary Truly Superb Glyph of Superb Glyph of Reduce Spell Cost is also accepted if you prefer to cast more abilities with your Magicka Pool (at cost of your DPS)

- For food, currently using Orzorga's Red Frothgar. Boosts Health and gives a good bunch of Magicka Recovery

- Last but not least, Essence of Spell Power made from Corn Flower and Lady's Smock with Lokhan's Tears as solvent is your best bet as it recovers Magicka and boosts your Spell Power