Azumarill is not an indomitable foe for Hydreigon.
Hydreigon @ Expert Belt
Rash, 4 Atk 252 SpA 252 Spe
Draco Meteor
Fire Blast
Superpower
Charge Beam
It requires a bit of (basic) prediction, but an Expert Belt-boosted Charge Beam hits max HP Azumarill quite hard as it switches in:
252+ SpA Expert Belt Hydreigon Charge Beam vs. 252 HP / 0 SpD Azumarill: 170-202 (42 - 50%) -- 0.4% chance to 2HKO
But don't forget Charge Beam's 70% chance of boosting Hydreigon's Special Attack. At +1, Hydreigon can dispose of Azumarill with ease:
+1 252+ SpA Expert Belt Hydreigon Charge Beam vs. 252 HP / 0 SpD Azumarill: 254-300 (62.8 - 74.2%) -- guaranteed 2HKO
And chances are, you're now in possession of a +1 or +2 Hydreigon, with the opponent's main "counter" now removed from the equation.
Offensive Togekiss suffers the same fate. At +1 on the 2nd turn, Hydreigon 2HKOs it. If Stealth Rock is on the field, the boost is not needed:
+1 252+ SpA Expert Belt Hydreigon Charge Beam vs. 0 HP / 0 SpD Togekiss: 187-221 (60.1 - 71%) -- guaranteed 2HKO
252+ SpA Expert Belt Hydreigon Charge Beam vs. 0 HP / 0 SpD Togekiss: 125-149 (40.1 - 47.9%) -- guaranteed 2HKO after Stealth Rock
Hydreigon had zero counters in Generation 5. While that no longer hold true in Gen 6, Pokemon that can safely switch in against him remain few and far between.