The biggest thing you need to understand about Hydra is the mechanics and how champs interact with them. Unlike CB, Hydra really isn't a "run it on auto", at least not until you understand what's going on. Essentially there are four main things you need to deal with for Hydra to work properly:
1) Head of Decay
This is the one that tends to ruin most peoples' runs. Decay does two really terrible things to you if he isn't controlled. He removes ALL debuffs from ALL heads, AND he gives them all a turn-meter boost. That is very often simply the end of the run, especially when combined with what the other heads can do. There's only one way to control him - Provoke. So, just about every Hydra team, except the really top-end ones that just oneshot him every time, basically require Provoke.
From your roster, you have a bunch of options, but what it comes down to, and I'll repeat this throughout, is - do you have books. Because Provoke champs NEED to be booked on their Provoke skill, both to reduce the cooldown and increase the chance of landing.
Wixwell & Bivald are both solid choices, as Rat mentioned, but Wixwell will probably not work on auto, since there's no guarantee he targets Decay with his A1. Wix can also work unbooked, since his A1 on bosses is 80% x2, which is close enough to a guarantee.
2) Head of Mischief
He's the annoying one, and he can definitely ruin runs too, though he doesn't tend to do it with the same "oomph" as Decay. You deal with him in one of three ways. Either you have enough resist on everyone to just resist his buff-steal, or you have enough resist on one or two champs AND you can guarantee they always have the bost buffs, or you use block debuffs to just prevent his buff-stealing from being too problematic. The last option is the worst of them, because even though he won't steal your buffs, he'll still remove them and steal your turn-meter, which means he's getting more turns, and that means you're getting eaten faster.
Unfortunately for now you probably don't have the luxury of choice, so, as mentioned by Rat, just go with Uugo to place the block buffs, assuming you haven't got Lazarius booked on his A2.
3) Head of Torment
Definitely annoying, but he's less so because you can avoid attacking him for the most part. Still, it definitely helps to run Veil or Perfect Veil instead. If he's booked Loki can probably do the job best, if not, Drath is a solid choice.
4) Head of Blight
You need to deal with the poison cloud, or else everything else falls apart pretty fast. Fortunately you have Uugo for that already, so you're set.
So, with all that in mind, your team so far is looking like:
1) Wixwell
2) Uugo
3) Drath
That leaves room for three more people. You definitely need damage, and on the lower difficulties, that's best-done by just using direct face damage. Pick your best-geared champs. Ninja and Artak are very good choices. So is Rathalos, if you've got him booked. There's lots to choose from, but you probably want to pick your best two.
For the last slot, you'll want utility. Things that are very useful to bring are Speed Up, Speed Down, Acc Up, and Acc Down, so try to pick someone who can do multiple of those.