Often while using ice beam, aura sphere, eartquake on cynthia's garchomp, garchomp simply dodges it, despite the fact that they have 100% hitting chance. Why does this happen?
If Aura Sphere is missing then your game is glitched. Aura Sphere never misses, no matter what evasion modifiers your opponent has or what accuracy modifiers you have.
Is this battle during a Sandstorm? While I don't remember battling her during one, Cynthia's Garchomp has Sand Veil and it increases its evasion in a sand storm by 20%.
This is the only reason I can think of because moves like Ice Beam should not miss, unless your Pokemon has Hustle or your opponent's used a move like Flash to decrease your accuracy. Articuno's ability is Pressure, and at this stage an opponent should not be using accuracy reducing moves (they might still use evasion inducing ones), so Sand Veil is the only thing raising Garchomps evasion stat.
Cynthia
Sand Veil (ability)
These moves DO NOT have a 100% hitting chance. The "100" on the accuracy section is actually not a percentage.