Synthia is because she is the Pokemon champion.
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Your Rival
The Frontier Brains and the Champions.
The strongest Pokemon trainer is definitely trainer Red from Pokemon Soul Silver/Heart Gold. All his pokemons are above level 80, way stronger than Steven from Emerald, and Blue from Pokemon Leaf Green/Fire Red. Amanzio from Pokemon White/Black wifi.
The rival the third time you battle him in survival area
That depends on the trainer and the way the pokemon is used. The highest-level Pokemon found in the wild is Kyurem, at Level 75.