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It's not. I received an Eevee from Wonder Trade before the first gym and it already had Baby-Doll Eyes and it did not evolve upon level up. However, after I got lv2 affection in Pokemon-amie, after a level up it evolved to Sylveon.
Streamed me playing this on NeoGAF not too long ago.
MVP was a Pidgeot that was Poison/Ghost, that had Sonic Boom (seriously this move is broken so early on), Ember, Aurora Beam, and Confusion.
Gonna have to say, I currently used Butterfree for the start of my HG file, and he's just ridiculous in-game. A near-accurate Sleep Powder thanks to Compound Eyes seriously does wonders. It's also very useful for catching Pokemon since it's one of the earliest Pokemon who can inflict status in...