I don't see the purpose, at all, for removing currently exisiting pieces, even if they ARE more or less useless. Revamping them to have a new legendary? Sure. Removing? No.
Why does Frost Nova have damage on it? This forces you to pick the Frost Nova damage rune.
Not quite sure what the fantasy is that you are going for. Firebirds is pure fire, Vyr's is Archon, especially given that Vyr is the guy who invented Archon, Tel'Rasha, who was famous for his control over all facets of the elements, and his meteors, is multi-elemental+meteors. This is more like revamped Delseres, a man who attempting to utilize the control over time into crafting a powerful suit of armor. Only unified thing is, well, Hydras. Hydras and storms? Hydras and natural effects?
As for skill usage, you really don't have anything supporting Wave of Force besides, well, the set bonus. Nothing that makes Wave of Force deal increased damage, it essentially completely fulfills the role of a spender.
In addition, you have to have Hydra, Blizzard, Black Hole, a generator, Wave of Force, AND Familiar to get maximum benefit. Black Hole/Blizzard is required to further boost your Hydra damage, which is where the majority of your damage is coming from. Wave of Force is needed because you need a spender of some sort, given that this isn't a niche build. Familiar is needed because you are boosting its damage, and you generally have things boosting pet damage. Generator because you will be using arcane power, and Generators are needed to fill in the gap.
Overall, only thing I agree on is that Hydra does need a set (All classes currently have 1-3 abilities that have NO set interaction whatsoever). I have to disagree with your 4 piece bonus (It only provides a 10% damage reduction buff on a single target, and makes you immune to damage in big crowds), as well as you 6 piece (Should be changed to granting 200% extra damage to all skills, with supporting legendaries making you choose which skills to pick)