Instructions
Level up your team of six Pokemon to level 40 or greater. Clair's team of four Pokemon are level 38 and 41, so your monsters need to be at comparable or higher levels to have a chance of winning the battle.
Bring Pokemon that have a distinct advantage over her monsters. Clair uses a Gyarados, a pair of Dragaonair and a Kingdra. Gyrados is severely hurt by electric and rock attacks. The two Dragonair are weaker against ice and dragon moves. Kingdra only has one weakness and that is a dragon attack. Find a strong Pokemon that knows a decent dragon attack and the battle is much easier to win.
Develop a strategy to beat Clair's Pokemon. Along with using Pokemon attacks that are more effective against her beasts, use status-altering attacks that cause sleep, poison and paralysis. If her dragons are having difficulty retaliating with their violent attacks -- like "Hydro Pump" and "Dragon Pulse" -- you have a major advantage over her.