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three ways to get shiny Eevee (not including trading)
1) SR for the Eevee that Bebe gives you in Hearthome (1/8192 chance)
2) Breed for Eevee (1/8192 chance)
3) Pokeradar chain in Trophy Garden when "swarming" (if chain is at 40, chance I think goes to 1/64 or something like that)