Claire is the toughest, no doubt.
Gyrados: Never really struggled here. Ampharos usually takes it down before it can become a problem although Intimidate does play a crucial role.
Dragonair: This is the worst ever. It's pretty much her staller. ThunderWave becomes a huge problem and DragonPulse/FireBlast finish it off relatively quickly.
Dragonair: Not as bad as the first one but still a problem. ThunderWave/Dragon Pulse can become a pain especially when it preceded Kingdra.
Kingdra: I hate this one. It's a constant problem. It's got a great defence and attack, adding Smokescreen to increase loss of accuracy and then HydroPump and HyperBeam, this easily can wipe any of my teams out.
Whitney is a close second though.
Clefairy: No problem as long as I get rid of it quickly (which I usually do). CuteCharm and double slap start to become deadly and metronome is hit or miss.I've seen worse.
Miltank: The devil. It's got a great defence and Attract followed by Stomp just becomes a road to hell. MilkDrink is just a constant pain but it's easier to defeat than Clair's Kingdra.
Chuck and Blue and Morty are fairly tough but given the right team they cause no hassle at all.