So, I literally just finished defeating the Void Elemental (Part of the Arcanum part of Mirage questline) and I wanted to post what I did for anyone else who struggled with it and found the other tips online as unhelpful as I did.
Here's what I did: I have a set of equipment specifically focused on outgoing health boost (including a life mastery amulet, though this might be optional). Usually use it when questing with friends. The void elemental doesn't shield against ice or death. Monstrology lets you capture treasure card minions that are relatively high level. So I grabbed some of the gultures from the Oasis, rank 14 death minions, and focused exclusively on healing it and myself. Helps if you have a pet with Spritely. Three gultures later, and the elemental was defeated.
WARNING! This method is not for the faint of heart. Use only if absolutely every other strategy has failed you, because it will take you one to two hours for the gultures to whittle the elemental down. Also, I used about 300 mana, so be aware this is a battle of attrition you'll be going into.
I really hope you don't need to use this strategy, but after 7 other strategies failed, I was willing to play the long game on this supposedly simple gauntlet.
If you're a Myth wizard, this fight is built for you! I tend to use the bosses from the 2nd fight of Mirror Lake. With one AOE spell enchanted with the right Animus spell on it, you can get 4 monsters' worth of Animus for 1 spell and casting. This is a great way to get lots of monsters fast. Then, use however many of them you need as Myth can cast up to 3 at a time and fill up the fight circle making it 4 of you vs 1 of the elemental.