If I remember right X and Y have the horde mechanic so you can abuse that, I did that for a few shinies.
Also, I could be wrong about this, but I THINK that series also has an area under a bridge that has a 100% feebas spawn rate - I used that to farm a shiny feebas. It's been a very long time since then, so it could be a different generation.
Good lucky shiny hunting!
Edit: just did some research and it seems the Feebas spawn is on ORAS. So it seems the horde mechanic is the best way to cheese out some shinies the fastest.
IIRC chain fishing and pokéradar also had pretty decent shiny odds in that gen, but from personal experience I have to agree with Yokozuna that hordes are still better to find specific shinies - and they feel more "natural" as well, compared to the other two methods.
Oh yea I totally forgot about chain fishing. I got a shiny Relicanth like that, I forgot the details about it but it's totally doable.
Edt: thinking about it some more I think I used an octillery with suction cups as the ability? This makes it to where there will always be a bite when you cast.