If we have access to Ice Beam/Blizzard TMs by then, I'm planing on using a Vaporeon. With Vaporeon's usually overlooked but very high Sp. Attack, excellent HP and great Sp. Defense, paired with Hydreigon's lack of any hard-hitting moves that are super effective against Water types [the only electric moves it would be able to learn that do damage are Charge Beam, Shock Wave, and Thunder Fang and I HIGHLY DOUBT Lin's Hydreigon is going to have any of them since they've pretty weak and it has a far better selection of moves to choose from]. Even if we don't have access to those moves by then, Vaporeon still has the move Aurora Beam, which might not be the most powerful move but it can still get the job done in a pinch [and has the possibility of lowering Attack, should this Hydreigon end up being a mixed attacker].
We know it has Flash Canon [and I don't think this'll change by the time we fight it], so Fairy and Ice types are going to be hit hard. Obvious choices for it's other moves would probably be hard-hitting Special Attacks like Dark Pulse, Dragon Pulse/Draco Meteor, Focus Blast, Fire Blast/Heat Wave, Surf, or Earth Power. If it's moves are chosen to be more of a mixed attacker, which I don't think will be the case but it is a possibility, it'll probably have Outrage, Earthquake, or Head Smash. Checking it's moveset on Bulbapedia, we can say it won't know Dragon Dance - which I think we can all be grateful for.
I think it's a good idea to plan to face this both offensively and defensively, hence my choice of Vaporeon being my main counter. Should it not prove to be enough, I do have more offensive-centric counters [Espeon with Dazzling Gleam and Florges with Moon Blast] to finish the job, though if we DO end up getting access to either Ice Beam or Blizzard by then, I'm fairly certain Vaporeon will be able to do the job all by herself.