Q&A for How to Get Shiny Pokémon in Pokémon X and Y

For Pokémon found in tall grass, you can try chaining them with the Poké Radar; for those in water, you can chain fish. You should also research if the Pokémon can be found in a Friend Safari, as shiny encounters there are eight times more common. Finally, completing the National Pokédex rewards you with the Shiny Charm, an item that triples your odds of finding a shiny Pokémon and stacks with the chaining and fishing methods.

Bulbapedia is an excellent resource for determining which egg group your Pokémon belongs to.

You can only use the Poke Radar in grass or flowers.

Unfortunately, you cannot find the gun fossil in X and Y. In order to obtain a Genesect, you must trade for it or wait for an event where you will be gifted with one. You can also hack for it, but this is not recommended.