This build is very glassy!
It has good damage but requires Goldwrap with Boon of the Hoarder to stay alive.
There is also In-geom in the cube to synergise with the Nemesis Bracers to help keep up your 10 second cooldown reduction from elite kills.
You don't have to use Sage's set but for the extra DB it is worth it.
This build centres around doing quick kills especially to elite packs and triggering the 10 second cooldown reduction from the In-geom.
Clicking on shrines and pylons with trigger the Nemesis Bracers and spawn a yellow elite pack which helps with the downtime of In-geom.
Try to ensure that you have gold being picked up at all times (which can be seen in the bottom right corner) to ensure an insane armour bonus and invulnerability from Goldwrap.
Weapon and Offhand:
The Unstable Scepter wand can get up to 450% extra damage as it's secondary ability with an extra trigger. While Triumvirate receives up to 400% Arcane Orb damage increase which can stack 3 times from using signature spells. Together these two items make this build viable with insane Arcane Orb damage with Tal's set.
For the shoulders, Homing Pads are used for the ability to teleport back to town at the end of a rift uninterrupted.
Tal's full set is used, either via 5 piece and RORG in the cube or full 6 piece if Sage's isn't used.
Nilfur's Boast boots are used if Sage's isn't due to the increase in meteor damage which hit from the 2 piece bonus from Tal's set.
Tal's amulet is required for this build. For the rings, Focus and Restraint are used for their damage bonus as a resource generator and spender are used constantly with this build.
If you have a ten second In-geom which is better than the Unstable Scepter cube the scepter and use the In-geom instead.
For the armour Goldwrap is required due to the buld being glassy. If you aren't using Sage's set and equip a Goldwrap you could use something else, personally I feel Frostburn gauntlets with their 20% cold skills damage and 50% chance to freeze enemies would be the best choice.
If you don't use Sage's set and have all six pieces of Tal's equipped you could equip an Avarice Band in the cube for better gold pickup.
This build is very resource heavy so a topaz is used in the helm to help ensure that you don't run out of arcane power. Topazes are used in the armour and legs and an emerald in the weapon like most Intelligence class builds.
Once you enter a rift cast your Storm Armour and Familiar so they become active. Then cast each of the other four skills to bring up Tal's 4 elemental skill bonuses.
Make sure to cast Electrocute three times to have the Triumvirate bonus active and at three stacks, then alternate between Electrocute and casting Arcane Orb at enemies. You can use force move along with the left click to quickly cast your signature spell to ensure the stacks for Triumvirate stay at 3 for the duration of the rift.
If there is a gap between enemy packs cast Teleport which with the Illusionist passive skill will add 30% movement speed for 3 seconds. When In-geom is triggered you can cast Teleport a lot more often to get to larger packs or find elite packs to ensure In-geom is always triggered and make moving through the rift and killing the Rift Guardian quicker.
Sometimes you might be standing in the centre of a large group of enemies and casting Arcane Orb killing them all but the gold wont pickup, it is all sitting on the floor, (even your pet wont pickup gold). To fix this you have to move slightly to trigger the gold to be picked up. This happens sometimes and can easily trigger your second chance passive (Unstable Anomaly) as your gold pickup streak will finish and Goldwrap's armour bonus along with it.
When you kill the Rift Guardian make sure to have enemies nearby or gold nearby if your damage is a little low, that way you can pickup a bundle of gold to keep your gold pickup streak going and make it easier to kill the Rift Guardian without dying.
With the skills; it doesn't matter which Signature Spell you use and if you use Hydra or not. I just like the look of Hydra and it is a low cost skill. The main thing is to sure that you have a fire skill and a lightning skill. Arcane Orb's cold rune Frozen Orb does the most damage and it doesn't do it over time so it is more of a requirement. Teleport with Calamity is needed for mobility with Illusionist and for being the only damage dealing Teleport skill, dealing arcane damage.
Storm Armour - Power of the Storm is used for it's 3 arcane power cost reduction. This could be changed to Scramble for it's 25% movement bonus for 3 seconds when hit by melee or ranged attacks but you should have In-geom procced almost all of the rift allowing you to teleport more.
Familiar - Arcanot along with Astral Presence add a lot of arcane power regeneration which is why they are required for ease of playing.
I hope someone finds this build helpful, I was looking for a speed build for rifts for the Wizard and found Flash Fire too low on damage and too intensive to be able to do passively while watching tv.